Chapter 5 · Arithmetic Progressions

NCERT Class 10 Maths Exercise 5.2

All 20 questions of NCERT Class 10 Maths Exercise 5.2 (Arithmetic Progressions), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Fill in the ​blanks ​in the following ​table, given that $a$ is the first term, $d$ the ​common difference ​and $a_n$ the $n$-th term of the AP.

   1. (i)$a=7$, $d=3$, $n=8$, $a_n=?$
   2. (ii)$a=-18$, $d=?$, $n=10$, $a_n=0$
   3. (iii)$a=?$, $d=-3$, $n=18$, $a_n=-5$
   4. (iv)$a=-18.9$, $d=2.5$, $n=?$, $a_n=3.6$
   5. (v)$a=3.5$, $d=0$, $n=105$, $a_n=?$

   AP parameters with one missing value per row

   	$a$	$d$	$n$	$a_n$
   (i)	7	3	8	...
   (ii)	$-18$	...	10	0
   (iii)	...	$-3$	18	$-5$
   (iv)	$-18.9$	2.5	...	3.6
   (v)	3.5	0	105	...

   Show answer

   (i) $a_8=28$; (ii) $d=2$; (iii) $a=46$; (iv) $n=10$; (v) $a_{105}=3.5$.

   Step-by-step solution →
2. Q2
   Choose ​the correct choice in the following ​and justify:

   1. (i)30th term of the ​AP $10,7,4,\dots$ (A) 97 (B) 77 (C) $-77$ ​(D) $-87$
   2. (ii)11th ​term of ​the AP $-3,-\frac{1}{2},2,\dots$ (A) 28 (B) 22 (C) $-38$ (D) $-48\frac{1}{2}$
   Show answer

   (i) $a_{30}=-77$, option (C). (ii) $a_{11}=22$, option (B).

   Step-by-step solution →
3. Q3
   In the ​following APs, ​find ​the missing terms in the boxes: ​

   1. (i)$2,\square ,26$
   2. (ii)$\square ,13,\square ,3$
   3. (iii)$5,\square ,\square ,9\frac{1}{2}$ ​
   4. (iv)$-4,\square ,\square ,\square ,\square ,6$ ​
   5. (v)$\square ,38,\square ,\square ,\square ,-22$
   Show answer

   (i) $\square =14$; (ii) ${\square }_1=18,{\square }_2=8$; (iii) ${\square }_1=\frac{13}{2}=6.5,{\square }_2=8$; (iv) $-2,0,2,4$; (v) $53,23,8,-7$.

   Step-by-step solution →
4. Q4
   Which term of ​the ​AP: $3,8,13,18,\dots ,$ ​is ​78?
   Show answer

   $78$ is the $16$th term of the AP, so $n=16$.

   Step-by-step solution →
5. Q5
   Find the ​number ​of ​terms in each of the following ​APs:

   1. (i)$7,13,19,\dots ,205$ ​
   2. (ii)$18,15\frac{1}{2},13,\dots ,-47$
   Show answer

   (i) $n=34$; (ii) $n=27$.

   Step-by-step solution →
6. Q6
   Check whether $-150$ ​is ​a ​term ​of ​the AP: $11,8,5,2,\dots$
   Show answer

   No — solving gives $n=\frac{164}{3}$, which is not a whole number, so $-150$ is not a term of the AP.

   Step-by-step solution →
7. Q7
   Find the ​31st ​term ​of ​an AP whose 11th ​term is ​38 ​and the ​16th term is 73.
   Show answer

   The $31$st term of the AP is $178$.

   Step-by-step solution →
8. Q8
   An ​AP ​consists of 50 ​terms ​of which 3rd term ​is ​12 and the last term is 106. Find ​the 29th term.
   Show answer

   The $29$th term of the AP is $64$.

   Step-by-step solution →
9. Q9
   If the 3rd and the 9th ​terms of an ​AP ​are $4$ and $-8$ ​respectively, which term ​of ​this AP is zero?
   Show answer

   The $5$th term of the AP is zero.

   Step-by-step solution →
10. Q10
    The 17th term of an ​AP exceeds ​its 10th ​term by 7. Find ​the ​common ​difference.
    Show answer

    $d=1$.

    Step-by-step solution →
11. Q11
    Which ​term ​of ​the AP: $3,15,27,39,\dots$ ​will be 132 ​more than its 54th ​term?
    Show answer

    The $65$th term of the AP is $132$ more than its $54$th term.

    Step-by-step solution →
12. Q12
    Two APs have ​the same ​common ​difference. The difference between their ​100th terms ​is $100$. What is the ​difference ​between their 1000th terms?
    Show answer

    The difference between the $1000$th terms is also $100$.

    Step-by-step solution →
13. Q13
    How many ​three-digit ​numbers are ​divisible ​by 7?
    Show answer

    There are $128$ three-digit numbers divisible by $7$.

    Step-by-step solution →
14. Q14
    How ​many multiples ​of $4$ ​lie ​between $10$ and $250$?
    Show answer

    There are $60$ multiples of $4$ between $10$ and $250$.

    Step-by-step solution →
15. Q15
    For what ​value of $n$, are ​the $n$-th ​terms of two APs: $63,65,67,\dots$ ​and $3,10,17,\dots$ ​equal?
    Show answer

    The $13$th terms are equal, so $n=13$.

    Step-by-step solution →
16. Q16
    Determine ​the ​AP ​whose ​third term ​is $16$ ​and the $7$th ​term exceeds the $5$th term by $12$.
    Show answer

    The AP is $4,10,16,22,\dots$ (with $a=4$, $d=6$).

    Step-by-step solution →
17. Q17
    Find the 20th term from ​the ​last ​term ​of the ​AP : $3,8,13,\dots ,253$.
    Show answer

    The $20$th term from the last is $158$.

    Step-by-step solution →
18. Q18
    The ​sum ​of the $4$th ​and $8$th terms of an ​AP is $24$ and the ​sum of the $6$th and $10$th terms is $44$. Find the first ​three ​terms of the ​AP.
    Show answer

    With $a=-13$ and $d=5$, the first three terms of the AP are $-13,-8,-3$.

    Step-by-step solution →
19. Q19
    Subba Rao ​started work in ​1995 at an annual salary of Rs ​5000 and received an increment ​of Rs 200 each year. ​In which year did his ​income reach ​Rs 7000?
    Show answer

    His income reached Rs $7000$ in the year $2005$.

    Step-by-step solution →
20. Q20
    Ramkali ​saved Rs 5 ​in the ​first ​week ​of a ​year and ​then increased her weekly savings by Rs 1.75. If in the nth week, her weekly savings become Rs 20.75, find n.
    Show answer

    $n=10$: Ramkali's weekly saving becomes Rs $20.75$ in the $10$th week.

    Step-by-step solution →