Question

For a given G.P., if T₂ = 9 and T₅ = 243; then find S₄.

Answer 1

Here. T₂ = 9; T₅ = 243; S₄ =?

T = a. r^n-1

∴ T₂ = a r^2-1

∴ 9 = ar ………..(1)

T₅ = a r^5-1
∴ 243 = ar⁴ …………..(2)

Taking ratio of results (2) and (1)

\(\frac{243}{9}=\frac{ar^4}{ar}\)

∴ 27 = r³

∴ (3)³ = r3

∴ r = 3

Putting r = 3 In the result (1),

9 = 3a ∴ a = 3

Now, S_n =  (∴ r > 1)