Question

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

Answer 1

Answer:

4, 8, 16, 32, 64

Step-by-step 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)

$\frac{a_{1}r^{9} }{a_{1}r^{6} }$ = $\frac{2048}{256}$

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