Question

Find the common ratio and write out the first four terms of the geometric sequence (1.04)^n-1

IF NECESSARY, round decimals to 4 places.

Common ratio is _________

a1 = ______
a2 = ______
a3 = ______
a4 = ______

Answer 1

see explanation

Explanation:

the nth term of a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

`a_(n)` =
`(1.04)^(n-1)` ← is in this form

with a₁ = 1 and r = 1.04

then

a₁ = 1

a₂ =
`(1.04)^(2-1)` =
`1.04^(1)` = 1.04

a₃ =
`(1.04)^(3-1)` = 1.04² = 1.0816

a₄ =
`(1.04)^(4-1)` = 1.04³ = 1.1249 ( to 4 dec. places )