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 22 of 23

1. Q421 CBSE 2016
   Ramkali would require ₹ $5000$ for ​getting her daughter admitted in a school after a ​year. ​She saved ₹ $150$ in the first month and then ​increased her monthly savings by ₹ $50$ ​every month. ​Find, if ​she will be able to arrange the required ​money after $12$ months. Which value is reflected in her efforts?
   Show answer

   Yes. She saves $S_{12}=$ ₹$5100$ in $12$ months, which is more than the ₹$5000$ required, so she can arrange the money. Her effort reflects the value of thrift, regular saving and determination for her daughter's education.

   Step-by-step solution →
2. Q422 CBSE 2016
   The houses in a row are numbered consecutively from $1$ to $49$. Show ​that there ​exists a ​value of $X$ such that ​sum of numbers of houses ​preceding the house numbered $X$ is equal to ​sum of the numbers of houses following $X$.
   Show answer

   Such a house exists: $X=35$ (the sums before and after both equal $595$).

   Step-by-step solution →
3. Q423 CBSE 2016
   In a school, students decided of planting trees in and ​around the ​school ​to reduce ​air pollution. Each section ​of each class was asked to plant the number of trees equal to the number of their class. The school has ​classes from I to X ​with $4$ sections each. How many trees will be planted by the students? What value is reflected by ​the students?
   Show answer

   A total of $220$ trees will be planted. The students reflect the value of environmental awareness and social responsibility (caring for a pollution-free environment).

   Step-by-step solution →
4. Q424 CBSE 2016
   The houses ​in ​a row are ​numbered consecutively from $1$ to $49$. Show that there exists a ​value of $X$ ​such that sum of numbers of houses proceeding the house ​numbered $X$ is equal to ​sum of the numbers ​of houses following $X$.
   Show answer

   Such a house exists: $X=35$.

   Step-by-step solution →
5. Q425 CBSE 2016
   A thief runs ​with a uniform speed of $100$ m/minute. After one minute a policeman runs after ​the thief to catch him. He goes with ​a speed ​of $100$ m/minute in the first minute and ​increases his speed by $10$ m/minute every succeeding ​minute. After how many minutes the policeman will catch the thief.
   Show answer

   The policeman catches the thief $5$ minutes after he starts running.

   Step-by-step solution →
6. Q426 CBSE 2016
   Reshma wanted to save ​at least Rs $6,500$ for sending ​her daughter to school ​next year ​(after 12 months). She saved Rs $450$ in the first month and raised her savings by Rs $20$ every next ​month. How much will she be able to ​save in next 12 months? Will she be able to send her daughter to the ​school next year? What value is reflected in this question?
   Show answer

   Reshma saves Rs $6,720$ in 12 months. Since $6720>6500$, yes she can send her daughter to school next year. The value reflected is the habit of regular saving and a mother's concern for her daughter's education.

   Step-by-step solution →
7. Q427 CBSE 2016
   The houses in a row are numbered consecutively ​from $1$ to $49$. Show ​that there exists a value ​of $X$ such ​that ​the sum of ​the numbers of houses preceding the house numbered $X$ is ​equal to the sum of the numbers of the houses ​following $X$.
   Show answer

   $X=35$. The sum of house numbers $1$ to $34$ equals the sum of house numbers $36$ to $49$, both being $595$.

   Step-by-step solution →
8. Q428 CBSE 2015
   If ​the ​numbers $a-2$, $4a-1$ ​and $5a+2$ ​form an ​A.P., find ​the value ​of $a$.
   Show answer

   $a=1$

   Step-by-step solution →
9. Q429 CBSE 2015
   Find ​the $25^{\text{th}}$ ​term ​of the A.P. $-5,\frac{-5}{2},0,\frac{5}{2},\dots$
   Show answer

   $a_{25}=55$

   Step-by-step solution →
10. Q430 CBSE 2015
    If ​the sum ​of ​the first $n$ terms of an A.P. is given as $S_n=n(4n+1)$, ​find ​its $10^{th}$ ​term.
    Show answer

    The $10^{th}$ term is $a_{10}=77$.

    Step-by-step solution →
11. Q431 CBSE 2015
    The ​fourth term of an A.P. is $11$. The sum ​of the fifth ​and seventh terms of the A.P. ​is $34$. Find its common ​difference.
    Show answer

    Common difference $d=3$

    Step-by-step solution →
12. Q432 CBSE 2015
    Find the middle ​term of ​the A.P. $6,13,20,\dots ,216$.
    Show answer

    The middle term is the 16th term, $a_{16}=111$.

    Step-by-step solution →
13. Q433 CBSE 2015
    In ​an AP, if $S_5+S_7=167$ and $S_{10}=235$, then ​find the AP, ​where $S_n$ ​denotes the ​sum ​of its first $n$ terms.
    Show answer

    $a=1$, $d=5$; the AP is $1,6,11,16,\dots$

    Step-by-step solution →
14. Q434 CBSE 2015
    The $14^{\text{th}}$ term ​of ​an AP is twice its $8^{\text{th}}$ term. If its $6^{\text{th}}$ ​term ​is $-8$, then find the sum ​of ​its ​first $20$ terms.
    Show answer

    $a=2$, $d=-2$, and $S_{20}=-340$.

    Step-by-step solution →
15. Q435 CBSE 2015
    If the ​sum ​of the first $7$ terms ​of an A.P. is $112$ ​and that ​of its first $17$ ​terms is $697$, find the sum of its first $n$ terms.
    Show answer

    The sum of the first $n$ terms is $S_n=\frac{n(5n-3)}{2}$ (with $a=1$, $d=5$).

    Step-by-step solution →
16. Q436 CBSE 2015
    In an A.P., ​if ​the $12^{\text{th}}$ term is $-13$ and the sum ​of its ​first ​four terms ​is $24$, find the sum ​of its first ​ten terms.
    Show answer

    The sum of the first ten terms is $S_{10}=0$ (with $a=9$, $d=-2$).

    Step-by-step solution →
17. Q437 CBSE 2015
    If $S_n$ ​denotes ​the ​sum of ​first $n$ terms of ​an A.P., prove ​that $S_{12}=3(S_8-S_4)$.
    Show answer

    Both sides equal $12a+66d$, hence $S_{12}=3(S_8-S_4)$ is proved.

    Step-by-step solution →
18. Q438 CBSE 2015
    Find the middle ​term of the ​sequence formed by all three-digit numbers which leave a ​remainder $3$, when divided by $4$. ​Also find ​the sum of all ​numbers on both sides of the middle term ​separately.
    Show answer

    Middle term $=551$; sum of the 112 terms before it $=36400$; sum of the 112 terms after it $=87024$.

    Step-by-step solution →
19. Q439 CBSE 2015
    Ramkali required $\text{₹}2500$ after $12$ weeks to send her daughter ​to school. She saved $\text{₹}100$ ​in the first week ​and increased ​her ​weekly saving by $\text{₹}20$ every week. Find whether she will be able ​to send her daughter ​to school after $12$ weeks. What value is generated in the above ​situation?
    Show answer

    Yes. In $12$ weeks she saves $S_{12}=\text{₹}2520$, which is more than the required $\text{₹}2500$, so she can send her daughter to school. The situation reflects the value of educating a girl child, together with thrift and determination.

    Step-by-step solution →
20. Q440 CBSE 2015
    Find the $60^{\text{th}}$ ​term of the ​AP $8,10,12,\dots$, if it has a total ​of 60 ​terms and hence find the ​sum of its last ​10 terms.
    Show answer

    $a_{60}=126$; the sum of the last 10 terms is $1170$.

    Step-by-step solution →