Question

The 13th term of an AP is 4 times its 3rd term. If its 5th term is 16 then the sum of its first ten terms is ______.

विकल्प

• 150

• 175

• 160

• 135

Answer 1

The 13th term of an AP is 4 times its 3rd term. If its 5th term is 16 then the sum of its first ten terms is 175.

Explanation:

T₁₃ = 4 × T₃ 

⇒ a + 12d = 4(a + 2d) 

⇒ 3a – 4d = 0 

T₅ = 16

⇒ a + 4d = 16 

On solving (i) and (ii), we get a = 4 and d = 3 

`S_10 = 10/2 (2a + 9d)` 

= 5(2 × 4 + 9 × 3)

= 175