1. The numbers 7, x and 15 are in AP. Find x.
- A8
- B22
- C10
- D11
Show answer
Answer: D) 11
For three terms in AP the middle one is the average of the other two: x = (7 + 15)/2 = 11. 8 is 15 − 7; 22 forgets to halve.
Class 10 Properties and Selection of AP Terms — practice questions with answers
Algebra — Sequences · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. If x + 2, 3x and 4x + 1 are in AP, find x.
- A3
- B2
- C1
- D4
Show answer
Answer: A) 3
2(3x) = (x + 2) + (4x + 1), so 6x = 5x + 3 and x = 3. The terms are 5, 9, 13.
3. An AP has 20 terms. The 5th term from the beginning plus the 5th term from the end is 64. Find the sum of all 20 terms.
- A64
- B1,280
- C320
- D640
Show answer
Answer: D) 640
Terms equidistant from the ends have the same sum, so . .
4. 2, 5, 8 are in AP. What is the common difference of (5 + 8), (8 + 2), (2 + 5)?
- A−3
- B−6
- C6
- D3
Show answer
Answer: A) −3
The new terms are 13, 10, 7: a decreasing AP with common difference −3. In general if a, b, c are in AP then b + c, c + a, a + b are in AP with difference −d.
5. The digits of a three-digit number are in AP and add up to 15. Reversing the digits increases the number by 594. Find the number.
- A258
- B852
- C357
- D159
Show answer
Answer: A) 258
Digits 5 − d, 5, 5 + d (sum 15). Number = 100(5 − d) + 50 + (5 + d) = 555 − 99d; reversed = 555 + 99d. Difference 198d = 594, so d = 3: the number is 258 (and 852 − 258 = 594).
Practise all 50 questions free →
10 free questions a day without an account — unlimited with a free account.