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A student computed the 12th term of the AP 4, 10, 16, … as . What is the correct value, and where is the error?

Class 10Arithmetic ProgressionsAlgebra — Sequences
  • A76; the working is correct
  • B64; the multiplier should be (n - 2)
  • C70; the common difference should be 5, not 6
  • D70; the multiplier should be (n - 1) = 11, not 12

Step-by-Step Solution

is correct, but the formula is , not . So . Multiplying by adds one extra common difference.
Answer: D) 70; the multiplier should be (n - 1) = 11, not 12

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.

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