Question

Two terms of a geometric sequence are given. Find the first five terms. Please help asap

Answer 1

4, 8, 16, 32, 64

Explanation:

The nth term of a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

Given

a₇ = 256 and a₁₀ = 2048 , then

a₁
`r^(6)` = 256 → (1)

a₁
`r^(9)` = 2048 → (2)

Divide (2) by (1)

`(a_(1)r^(9) )/(a_(1)r^(6) )` =
`(2048)/(256)`

r³ = 8 ( take the cube root of both sides )

r =
`\sqrt[3]{8}` = 2

Substitute r = 2 into (1)

a₁ ×
`2^(6)` = 256

a₁ × 64 = 256 ( divide both sides by 64 )

a₁ = 4

Then

a₁ = 4

a₂ = 2a₁ = 2 × 4 = 8

a₃ = 2a₂ = 2 × 8 = 16

a₄ = 2a₃ = 2 × 16 = 32

a₅ = 2a₄ = 2 × 32 = 64