Question

The sum to infinity of a g.p is twice the first term. Find the eight term of the sequence

Answer 1

Answer:-

Given:-

Sum to infinity of a gp is twice the first term.

We know;

Sum of infinite terms in GP = a/1 - r

So,

⟹ a/1 - r = 2a

⟹ a = 2a (1 - r)

⟹ 1 = 2 - 2r

⟹ 2r = 2 - 1

⟹ r = 1/2

Now,

nth term of a GP (aₙ) = a × rⁿ⁻¹

⟹ a₈ = a × (1/2)⁸⁻¹

⟹ a₈ = a × 1/2⁷

⟹ a₈ = a/2⁷

∴ Eighth term of the given GP is a/2⁷.