Question

Write the first three terms of the G.P. whose first term and the common ratio are given below

a = `sqrt(2)`, r = `sqrt(2)`

Answer 1

a = `sqrt(2)`, r = `sqrt(2)`

t_n = ar^n–1

t₁ = ar^1–1 = ar⁰ = `sqrt(2) xx 1 = sqrt(2)`

t₂ = ar^2–1 = ar¹ = `sqrt(2) xx sqrt(2)` = 2

t₃ = ar^3–1 = ar² = `sqrt(2) xx (sqrt(2))^2`

= `sqrt(2) xx 2 = 2sqrt(2)`

∴ The 3 terms are `sqrt(2), 2, 2sqrt(2), ...`