Chapter 5 · Arithmetic Progressions

NCERT Exemplar Class 10 Maths Exercise 5.1

All 18 questions of NCERT Exemplar Class 10 Maths Exercise 5.1 (Arithmetic Progressions), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   In ​an ​AP, ​if $d=-4$, $n=7$, $a_n=4$, then $a$ is

   1. (a)$6$
   2. (b)$7$
   3. (c)$20$
   4. (d)$28$
   Show answer

   (d) $28$

   Step-by-step solution →
2. Q2
   In an ​AP, ​if $a=3.5$, $d=0$, $n=101$, ​then $a_n$ will be

   1. (a)$0$
   2. (b)$3.5$
   3. (c)$103.5$
   4. (d)$104.5$
   Show answer

   (b) $3.5$

   Step-by-step solution →
3. Q3
   The list ​of ​numbers $-10,-6,-2,2,\dots$ is

   1. (a)an AP with $d=-16$
   2. (b)an AP with $d=4$
   3. (c)an AP with $d=-4$
   4. (d)not an AP
   Show answer

   (b) an AP with $d=4$

   Step-by-step solution →
4. Q4
   The 11th ​term ​of the ​AP: $-5,-\frac{5}{2},0,\frac{5}{2},\dots$ ​is

   1. (a)$-20$
   2. (b)$20$
   3. (c)$-30$
   4. (d)$30$
   Show answer

   (b) $20$

   Step-by-step solution →
5. Q5
   The first ​four ​terms of an AP, ​whose first term is $-2$ and ​the common difference is $-2$, ​are

   1. (a)$-2,0,2,4$
   2. (b)$-2,4,-8,16$
   3. (c)$-2,-4,-6,-8$
   4. (d)$-2,-4,-8,-16$
   Show answer

   (c) $-2,-4,-6,-8$

   Step-by-step solution →
6. Q6
   The $21^{st}$ ​term ​of the ​AP ​whose first ​two terms ​are $-3$ and $4$ ​is

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

   (b) 137

   Step-by-step solution →
7. Q7
   If the 2nd term ​of an AP ​is ​13 and ​the 5th ​term is ​25, ​what ​is its 7th term?

   1. (a)30
   2. (b)33
   3. (c)37
   4. (d)38
   Show answer

   (b) 33

   Step-by-step solution →
8. Q8
   Which ​term of the ​AP: 21, ​42, ​63, ​84, ​... is 210?

   1. (a)9th
   2. (b)10th
   3. (c)11th
   4. (d)12th
   Show answer

   (b) 10th

   Step-by-step solution →
9. Q9
   If the ​common ​difference ​of an AP ​is $5$, ​then what is $a_{18}-a_{13}$?

   1. (a)5
   2. (b)20
   3. (c)25
   4. (d)30
   Show answer

   (c) 25

   Step-by-step solution →
10. Q10
    What ​is ​the ​common difference ​of an AP ​in which $a_{18}-a_{14}=32$?

    1. (a)$8$
    2. (b)$-8$
    3. (c)$-4$
    4. (d)$4$
    Show answer

    (a) $8$

    Step-by-step solution →
11. Q11
    Two ​APs have the same common difference. The first ​term ​of ​one of these is $-1$ and that of the other is $-8$. Then the difference ​between their 4th ​terms ​is

    1. (a)$-1$
    2. (b)$-8$
    3. (c)$7$
    4. (d)$-9$
    Show answer

    (c) $7$

    Step-by-step solution →
12. Q12
    If ​7 ​times ​the $7^{\text{th}}$ term ​of an ​AP is equal to 11 times its $11^{\text{th}}$ term, ​then ​its 18th term will be

    1. (a)$7$
    2. (b)$11$
    3. (c)$18$
    4. (d)$0$
    Show answer

    (d) $0$

    Step-by-step solution →
13. Q13
    The ​4th ​term ​from ​the end ​of the ​AP: $-11,-8,-5,\dots ,49$ is

    1. (a)$37$
    2. (b)$40$
    3. (c)$43$
    4. (d)$58$
    Show answer

    (b) $40$

    Step-by-step solution →
14. Q14
    The famous ​mathematician associated ​with ​finding the sum of ​the first 100 ​natural ​numbers is

    1. (a)Pythagoras
    2. (b)Newton
    3. (c)Gauss
    4. (d)Euclid
    Show answer

    (c) Gauss

    Step-by-step solution →
15. Q15
    If the ​first ​term of an AP is $-5$ and the common ​difference is $2$, ​then the ​sum ​of the ​first $6$ terms is

    1. (a)$0$
    2. (b)$5$
    3. (c)$6$
    4. (d)$15$
    Show answer

    (a) $0$

    Step-by-step solution →
16. Q16
    The ​sum ​of ​first ​16 ​terms ​of the AP: $10,6,2,\dots$ ​is

    1. (a)$-320$
    2. (b)$320$
    3. (c)$-352$
    4. (d)$-400$
    Show answer

    (a) $-320$

    Step-by-step solution →
17. Q17
    In ​an ​AP ​if $a=1$, $a_n=20$ and $S_n=399$, ​then $n$ ​is

    1. (a)19
    2. (b)21
    3. (c)38
    4. (d)42
    Show answer

    (c) 38

    Step-by-step solution →
18. Q18
    The ​sum ​of first ​five ​multiples ​of ​3 is

    1. (a)45
    2. (b)55
    3. (c)65
    4. (d)75
    Show answer

    (a) 45

    Step-by-step solution →