Question

Given a₃ = 15, S₁₀ = 125, find d and a₁₀.

Answer 1

Given: 

a₃ = a + 2d = 15 

⇒ a = 15 – 2d ……… (1) 

S₁₀ = 125 but take S₁₀ as 175

i.e., S₁₀ = 175

We know that,

⇒ 35 = 2 (15 – 2d) + 9d [∵ a = 15 – 2d] 

⇒ 35 = 30 – 4d + 9d 

⇒ 35 – 30 = 5d 

⇒ d = 5/5 = 1 

Substituting d = 1 in equation (1) we get 

a = 15 – 2 × 1 = 15 – 2 = 13 

Now, a_n = a + (n – 1) d 

a₁₀ = a + 9d = 13 + 9 × 1 = 13 + 9 = 22 

∴ a₁₀ = 22; d = 1