Class 10 Maths · Chapter 5

Arithmetic Progressions

441 Class 10 Maths questions on Arithmetic Progressions from the NCERT textbook, NCERT Exemplar and CBSE board papers 2015–2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 8 of 23

1. Q141 CBSE 2026
   The ​sum ​of first $n$ ​terms ​of ​an A.P. is $2n^2+13n$. Find its $n^{\text{th}}$ term ​and ​hence $10^{\text{th}}$ ​term.
   Show answer

   The $n^{\text{th}}$ term is $a_n=4n+11$, and hence the $10^{\text{th}}$ term is $a_{10}=51$.

   Step-by-step solution →
2. Q142 CBSE 2026
   In ​an A.P., ​it is ​given that $a=2$, $d=8$ and $S_n=90$. ​Find ​the ​value of $n$.
   Show answer

   $n=5$.

   Step-by-step solution →
3. Q143 CBSE 2026
   How ​many $4$-digit numbers ​are ​divisible ​by $7$?
   Show answer

   There are $1286$ four-digit numbers divisible by $7$.

   Step-by-step solution →
4. Q144 CBSE 2026
   The third and ninth term ​of an ​A.P. are $4$ and $-8$ ​respectively.

   1. (i)Which ​term of the A.P. is ​zero? ​
   2. (ii)Find ​the value of $n$ if $S_n=-36$.
   Show answer

   (i) The $5$th term of the A.P. is zero. (ii) $n=12$.

   Step-by-step solution →
5. Q145 CBSE 2026
   In a potato race, a bucket is ​placed at the ​starting ​point, which is $5$ m from the first potato. The other potatoes are arranged $3$ ​m apart in a straight ​line, with a total of $10$ potatoes, as shown in the figure : A competitor starts from the bucket, picks up ​the nearest potato, runs ​back to the bucket to drop it in, then returns to pick up the next potato. This process continues until all the potatoes are in the bucket. Based on the above information, answer the following questions :

   1. (i)What is the distance covered to pick up the first potato and drop it in bucket ?[1]
   2. (ii)What is the distance covered to pick up the second potato and drop it in bucket ?[1]
   3. (iii)(a)What is the total distance the competitor has to run ?[2]
   4. (iii)(b)OR : If average speed of competitor is $5$ m/s, then find the average time taken by competitor to put all the potatoes in the bucket.[2]
   Show answer

   (i) The distance covered for the first potato is $10$ m; (ii) The distance covered for the second potato is $16$ m; (iii)(a) The total distance the competitor has to run is $370$ m; (iii)(b) The average time taken is $74$ seconds.

   Step-by-step solution →
6. Q146 CBSE 2026
   Case Study - 1 Your elder brother ​wants to buy a car and plans to take a ​loan ​from a bank for his car. He repays his total loan of ₹ $1,18,000$ by paying every ​month, starting with ​the first instalment of ​₹ $1,000$ ​and he increases the instalment by ₹ $100$ every month. Based on ​the information given above, answer the following questions :

   1. (i)Find the amount paid by him in the $30^{\text{th}}$ instalment.[1]
   2. (ii)If the total number of instalments is $40$, what is the amount paid in the last instalment ?[1]
   3. (iii)(a)What amount does he still have to pay after the $30^{\text{th}}$ instalment ?[2]
   4. (iii)(b)(OR) Find the ratio of the tenth instalment to the last instalment.[2]
   Show answer

   (i) The amount paid in the $30^{\text{th}}$ instalment is ₹ $3,900$; (ii) The amount paid in the last ($40^{\text{th}}$) instalment is ₹ $4,900$; (iii)(a) The amount still to be paid after the $30^{\text{th}}$ instalment is ₹ $44,500$; (iii)(b) The ratio of the tenth instalment to the last instalment is $19:49$.

   Step-by-step solution →
7. Q147 CBSE 2026
   The best athlete of ​your school ​wants to participate ​in a $300$ m race in a state championship. Presently he can run that distance in $60$ seconds but ​is confident that with each day of practice it will take him $3$ seconds less ​than the previous day. So, first day he ​will take $60$ seconds, $2^{\text{nd}}$ day $57$ seconds, third day $54$ seconds and so on, to complete the race. He wants to do it in $30$ ​seconds. Based on the above, answer the following questions :

   1. (i)Write the first five terms of time and show that it forms an A.P.[1]
   2. (ii)How much time he will take on $6^{\text{th}}$ day to complete the race ?[1]
   3. (iii)(a) On which day he will be able to achieve his target of $30$ seconds ? OR (b) If he devotes more time in practice and that may take him $3.2$ seconds less than the previous day in completing the race, then on which day he will be able to complete the race in $28$ seconds ?[2]
   Show answer

   (i) The times are $60,57,54,51,48$ seconds; the constant difference $-3$ makes it an A.P. (ii) On the $6^{\text{th}}$ day he takes $45$ seconds. (iii) (a) He achieves $30$ seconds on the $11^{\text{th}}$ day; OR (b) with $d=-3.2$ s he completes the race in $28$ seconds on the $11^{\text{th}}$ day.

   Step-by-step solution →
8. Q148 CBSE 2026
   A watermelon vendor arranged the watermelons similar ​to shown in ​the ​adjoining picture : The number ​of watermelons in subsequent rows differ by '$d$'. ​The bottommost row has $101$ watermelons and the topmost row has $1$ watermelon. There are $21$ rows from ​bottom to top. Based on the above information, answer the ​following questions :

   1. (i)Find the value of '$d$'.[1]
   2. (ii)How many watermelons will be there in the $15$th row from the bottom ?[1]
   3. (iii)(a)Find the total number of watermelons from bottom to top.[2]
   4. (iii)(b)OR : If the number of watermelons in the $n$th row from top is equal to number of watermelons in the $n$th row from bottom, find the value of $n$.[2]
   Show answer

   (i) $d=-5$; (ii) The $15$th row from the bottom has $31$ watermelons; (iii)(a) The total number of watermelons is $1071$; (iii)(b) $n=11$.

   Step-by-step solution →
9. Q149 CBSE 2026
   A multistorey building is constructed with stilt ​parking. There is a provision of lift, as well as ​staircase from the ground floor to the top floor. The number ​of stairs from ​the ground floor ​to the first floor is $10$, from the first floor ​to the second ​floor is $24$, from ​the second floor to the third floor is $38$, and so on. Based on the above information, answer the following questions :

   1. (i)Does $10,24,38,\dots$ form an A.P. ? Justify your answer.[1]
   2. (ii)What will be the total number of stairs from the ground floor to the eleventh floor ?[1]
   3. (iii)(a)A person supplies water cans to people living in the building. As water cans are heavy, he supplies water cans on each floor, carrying one at a time. He supplied the water can from the ground floor to the first floor, came back and supplied water can to the second floor, again came back then supplied water can to the third floor, and so on. (a) Find the total number of stairs he climbed up and down to supply water till the sixth floor, using A.P.[2]
   4. (iii)(b)OR : The next day, following the same process, if a person climbed up and down a total of $380$ stairs, till which floor did he supply water cans ?[2]
   Show answer

   (i) Yes — the differences are $24-10=14$ and $38-24=14$, which are equal, so $10,24,38,\dots$ forms an A.P. with common difference $14$; (ii) The total number of stairs from the ground floor to the eleventh floor is $880$; (iii)(a) The total number of stairs climbed up and down to supply water till the sixth floor is $1400$; (iii)(b) He supplied water cans till the $3^{\text{rd}}$ floor.

   Step-by-step solution →
10. Q150 CBSE 2026
    A city based ​NGO ​is organising a competition to break 'Dahi Handi' by forming a human pyramid on the occasion of Janmashtami. One troop with $400$ members decided to participate ​in the competition. ​They planned to build eleven level pyramid with level one ​being at the bottom and ​level eleven being at the top. Level one has $41$ members, level two has $37$ ​members, level three has $33$ members ​and so on. Based on the above information, answer the following questions :

    1. (i)What is the number of members at level eleven ?[1]
    2. (ii)Find the number of members at the third level from the top.[1]
    3. (iii)(a)Find the total number of members who formed the human pyramid.[2]
    4. (iii)(b)OR : At which level is the number of members $5$ times the number of members at level ten ?[2]
    Show answer

    (i) Level eleven has $1$ member; (ii) The third level from the top (level $9$) has $9$ members; (iii)(a) The pyramid is formed by $231$ members in all; (iii)(b) Level $5$ has $5$ times the members of level ten ($25=5\times 5$).

    Step-by-step solution →
11. Q151 CBSE 2026
    'Kolam' ​is a decorative art which is made with rice flour in South Indian States. It is drawn ​on ​grid pattern ​of dots. One such art work ​is shown below. Observe the given figure carefully. There are $4$ dots in first square, $8$ dots in ​second square, $12$ dots in third square and so on. Based on the ​above, answer the following ​questions :

    1. (i)Show that number of dots given above form an A.P. Write the first term and common difference.[1]
    2. (ii)Write $n^{\text{th}}$ term of the A.P. formed.[1]
    3. (iii) (a)The pattern is expanded on a large ground. If total $220$ dots are used, then find the number of squares formed.[2]
    4. OR (iii) (b)Is it possible to complete $n$ number of squares using $100$ dots ? If yes, then find the value of $n$.[2]
    Show answer

    (i) The counts $4,8,12,\dots$ form an A.P. with first term $a=4$ and common difference $d=4$. (ii) $a_n=4n$. (iii)(a) $2n(n+1)=220$ gives $n=10$, so $10$ squares are formed. (iii)(b) No; $2n(n+1)=100$ gives $n(n+1)=50$, which has no positive integer solution, so $100$ dots cannot complete a whole number of squares.

    Step-by-step solution →
12. Q152 CBSE 2026
    A friend of yours ​wants to buy an electric car, for which he ​plans to take a loan from a bank and repay the ​total ​loan ​and interest, $\text{₹}5,90,000$, by paying every month. He starts with a ​first instalment of $\text{₹}5,000$ and increases the instalment ​by $\text{₹}500$ every month.

    1. (a)What are the first three instalments paid by him?[1]
    2. (b)Find the amount to be paid by him in the $11^{\text{th}}$ instalment.[1]
    3. (c)Find the number of instalments in which he would clear his total loan. OR After paying the $31^{\text{st}}$ instalment, find how much money he still has to pay.[2]
    Show answer

    (a) The first three instalments are $\text{₹}5000$, $\text{₹}5500$ and $\text{₹}6000$. (b) The $11^{\text{th}}$ instalment is $\text{₹}10,000$. (c) He clears the loan in $40$ instalments; OR, after the $31^{\text{st}}$ instalment he still has to pay $\text{₹}2,02,500$.

    Step-by-step solution →
13. Q153 CBSE 2025
    If the ​first term ​of ​an A.P. is ​'a' ​and ​its common difference is 'b', then its $10^{th}$ ​term ​is :

    1. (a)$a+10b$
    2. (b)$10a+b$
    3. (c)$a+9b$
    4. (d)$9a+b$
    Show answer

    (c) $a+9b$

    Step-by-step solution →
14. Q154 CBSE 2025
    The $22^{\text{nd}}$ ​term ​of the A.P. $\frac{3}{2},\frac{1}{2},-\frac{1}{2},-\frac{3}{2},\dots$ is

    1. (a)$\frac{45}{2}$
    2. (b)$-9$
    3. (c)$-\frac{39}{2}$
    4. (d)$-21$
    Show answer

    (c) $-\frac{39}{2}$

    Step-by-step solution →
15. Q155 CBSE 2025
    If $n$-th ​term of an A.P. ​is $5n-6$, then ​its ​common difference ​is ​:

    1. (a)$-6$
    2. (b)$5n$
    3. (c)$5$
    4. (d)$6$
    Show answer

    (c) $5$

    Step-by-step solution →
16. Q156 CBSE 2025
    If ​the first term of an A.P. is $-12$ and the ​common ​difference is $4$, then ​the ​sum ​of its first $7$ terms is

    1. (a)$-24$
    2. (b)$-48$
    3. (c)$0$
    4. (d)$48$
    Show answer

    (c) $0$

    Step-by-step solution →
17. Q157 CBSE 2025
    The $6^{\text{th}}$ term of ​the ​AP $\sqrt{27},\sqrt{75},\sqrt{147},\dots$ ​is ​:

    1. (a)$\sqrt{243}$
    2. (b)$\sqrt{363}$
    3. (c)$\sqrt{300}$
    4. (d)$\sqrt{507}$
    Show answer

    (d) $\sqrt{507}$

    Step-by-step solution →
18. Q158 CBSE 2025
    $10^{\text{th}}$ term of ​the ​A.P. $-12,-19,-26,\dots$ ​is

    1. (a)$-75$
    2. (b)$-65$
    3. (c)$51$
    4. (d)$-82$
    Show answer

    (a) $-75$

    Step-by-step solution →
19. Q159 CBSE 2025
    The sum of ​three terms in ​A.P. is $30$. ​If the greatest ​term is $13$, ​then ​the common difference is

    1. (a)$2$
    2. (b)$3$
    3. (c)$-2$
    4. (d)$-3$
    Show answer

    (b) $3$

    Step-by-step solution →
20. Q160 CBSE 2025
    The $21^{st}$ term of an ​AP ​whose ​first ​two terms are $-3$ ​and $4$ ​respectively, ​is:

    1. (a)$17$
    2. (b)$143$
    3. (c)$137$
    4. (d)$153$
    Show answer

    (c) $137$

    Step-by-step solution →