- A5
- B3
- C4
- D8
Step-by-Step Solution
→ → → . Check with the AP 3, 7, 11, …: .
Answer: C) 4
The first term of an AP is 3 and the sum of its first 9 terms is 171. Find its common difference.
Class 10Arithmetic ProgressionsAlgebra — Sequences
Key idea: n-th term formula
**aₙ = a + (n − 1)d**
Where a is the first term, d is the common difference, n is the position.
**Why**: a₁ = a; a₂ = a + d; a₃ = a + 2d; … aₙ = a + (n − 1)d. Each step adds another d.
**Example**: AP 3, 7, 11, 15, …. Find the 20th term.
a = 3, d = 4. a₂₀ = 3 + 19·4 = 79.
**Reverse use**: 'In the AP 5, 11, 17, …, which term is 89?' a + (n−1)d = 89 → 5 + 6(n−1) = 89 → n = 15.
Where a is the first term, d is the common difference, n is the position.
**Why**: a₁ = a; a₂ = a + d; a₃ = a + 2d; … aₙ = a + (n − 1)d. Each step adds another d.
**Example**: AP 3, 7, 11, 15, …. Find the 20th term.
a = 3, d = 4. a₂₀ = 3 + 19·4 = 79.
**Reverse use**: 'In the AP 5, 11, 17, …, which term is 89?' a + (n−1)d = 89 → 5 + 6(n−1) = 89 → n = 15.
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All Arithmetic Progressions practice questions
More Class 10 Arithmetic Progressions practice
At a timber depot, logs are stacked so that the bottom row has 20 logs, the row above it…A concrete platform has 10 steps, as shown. Every step is 2 m long, has a tread of ½ m,…In a potato race at a school sports day, a bucket is placed at the start. The first…Dots are arranged in triangles as shown. Do the numbers of dots in Figures 1, 2, 3, 4, ……A carpenter makes the ladder shown. Its rungs are 20 cm apart and shrink evenly from 50…