About Arithmetic & Geometric Progression — Class 10 ICSE

Find nth terms and sums of arithmetic and geometric progressions with applications. This topic is part of the ICSE Class 10 mathematics syllabus (chapter: Chapter 11). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 10-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Arithmetic & Geometric Progression — solved examples for Class 10 ICSE

Practice questions on Arithmetic & Geometric Progression

1. Q1.easy

   The common difference of the AP $7, 11, 15, 19, \ldots$ is:

   1. A)$3$
   2. B)$4$
   3. C)$7$
   4. D)$-4$
   Show answer

   Answer: $4$

   Hint: Common difference = second term minus first term.

2. Q2.easy

   The $n$th term of an AP with first term $a$ and common difference $d$ is:

   1. A)$a + nd$
   2. B)$a + (n-1)d$
   3. C)$a \times d^{n-1}$
   4. D)$a \times d^n$
   Show answer

   Answer: $a + (n-1)d$

   Hint: The first term has 0 differences added, the second has 1, the nth has (n-1).

3. Q3.easy

   Find the $10$th term of the AP $3, 7, 11, 15, \ldots$

   1. A)$39$
   2. B)$37$
   3. C)$35$
   4. D)$41$
   Show answer

   Answer: $39$

   Hint: Use $a_n = a + (n-1)d$ with $a = 3$, $d = 4$, $n = 10$.

4. Q4.medium

   If the $5$th term of an AP is $19$ and the $10$th term is $34$, find the first term.

   1. A)$5$
   2. B)$7$
   3. C)$3$
   4. D)$9$
   Show answer

   Answer: $7$

   Hint: $a_5 = a + 4d = 19$ and $a_{10} = a + 9d = 34$. Subtract to find d first.

5. Q5.medium

   The $4$th term of a GP is $24$ and the $7$th term is $192$. Find the common ratio.

   1. A)$2$
   2. B)$3$
   3. C)$4$
   4. D)$\frac{1}{2}$
   Show answer

   Answer: $2$

   Hint: $\frac{a_7}{a_4} = r^3$.

6. Q6.medium

   Find the sum: $1 + 3 + 5 + 7 + \ldots + 99$.

   1. A)$2500$
   2. B)$2450$
   3. C)$2550$
   4. D)$2400$
   Show answer

   Answer: $2500$

   Hint: This is an AP of odd numbers. Find n first, then use the sum formula.

7. Q7.hard

   If the sum of the first $p$ terms of an AP is equal to the sum of the first $q$ terms (where $p \neq q$), then the sum of the first $(p+q)$ terms is:

   1. A)$p + q$
   2. B)$pq$
   3. C)$0$
   4. D)$2(p+q)$
   Show answer

   Answer: $0$

   Hint: Set $S_p = S_q$ and use the sum formula. Then find $S_{p+q}$.

8. Q8.hard

   The ratio of the sums of $n$ terms of two APs is $(7n+1):(4n+27)$. The ratio of their $11$th terms is:

   1. A)$4:3$
   2. B)$148:111$
   3. C)$71:55$
   4. D)$7:4$
   Show answer

   Answer: $4:3$

   Hint: The ratio of nth terms = the ratio of sums evaluated at $m$ where $a_m$ = $a_{11}$, i.e., at $n = 21$.

9. Q9.hard

   If $S_n$ denotes the sum of $n$ terms of an AP whose $r$th term is $a_r$, then $S_n - 2S_{n-1} + S_{n-2}$ equals:

   1. A)$a_n$
   2. B)$2a_n$
   3. C)$d$
   4. D)$0$
   Show answer

   Answer: $0$

   Hint: $S_n - S_{n-1} = a_n$ and $S_{n-1} - S_{n-2} = a_{n-1}$. So the expression = $a_n - a_{n-1}$... but wait, is it?

These are 9 of the 60 questions available for Arithmetic & Geometric Progression. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.