Question

How do you write the first five terms of the geometric sequence `a_1=5, r=2x`?

Answer 1

`5, 10x, 20x^2,40x^3,80x^4`

Explanation:

Given
`color(white)("XXX")a_1=5`
By definition of geometric sequence
`color(white)("XXX")a_n=a_(n-1)xxr`
Therefore
`color(white)("XXX")a_2=a_1xxr=5xx2x=10x`

`color(white)("XXX")a_3=a_2xxr=10xx2x=20x^2`

`color(white)("XXX")a_4=a_3xxr=20x^2xx2x=40x^3`

`color(white)("XXX")a_5=a_4xxr=40x^3xx2x=80x^4`