Let a₁, a₂ 2 , a₃ 2² , , a₁₀ 2⁹ be a G.P. of common ratio 1 2 . If a₁+a₂+ +a₁₀=62 , then a₁ is equal to :

Step-by-step solution

The G.P. is a₁, a₂ 2 , a₃ 2^2 , , a₁₀ 2^9 with common ratio 1 2 . So a_n 2^ n-1 = a₁ ( 1 2 )^ n-1 , giving a_n = a₁ ( 2 )^ n-1 . _ n=1 ¹⁰ a_n = a₁ ( 2 )¹⁰ - 1 2 - 1 = a₁ 31 2 - 1 = 31a₁( 2 + 1) . Setting this equal to 62: a₁ = 2 2 +1 = 2( 2 -1) .