Question

If in an AP, a = 2 and S₁₀ = 335, then its 10th term is ______.

Options

• 55

• 65

• 68

• 58

Answer 1

If in an AP, a = 2 and S₁₀ = 335, then its 10th term is 65.

Explanation:

In a given AP, first term, a = 2 and sum of first 10 terms, S₁₀ = 335

Since, S_n = `n/2[2a + (n - 1)d]`

∴ S₁₀ = `10/2[2 xx 2 + (10 - 1)d]`

∴ 335 = 5[4 + 9d]

∴ 4 + 9d = 67

∴ 9d = 63

∴ d = `63/9`

∴ d = 7

∴ Common difference, d = 7

Also, n^th term a_n = a + (n - 1)d

∴ a₁₀ = a + (10 - 1)d

= a + 9d

= 2 + 9 × 7

= 2 + 63

= 65

Hence, the 10^th term is 65.