Question

n^th term of an A.P. is a_n . If a₁ + a₂ + a₃ = 102 and a₁ = 15, then find a₁₀ .

Answer 1

Given a₁ = 15 and a₁ + a₂ + a₃ =102 

a + a + d + a + 2d = 102

⇒ 3a + 3d = 102 

⇒ 3 (a + d) = 102 

∴ (a + d) = 102/3 = 34 

⇒ d = 34 – a = 34 – 15 = 19 

∴ a = 15, 0 = 19 

then its 10^th term = a₁₀ 

= a + (10 – 1)d 

= a + 9d = 15 + 9(19) 

= 15 + 171 = 186 

∴ 10^th term of it = 186