Question

Find the 7th term of the geometric sequence shown below
10x^3, 40x^8, 160x^13,…

Answer 1

`a_7=40960x^(33)`

Explanation:

Geometric sequence has explicit form:

`a_n=a \cdot r^(n-1)` where
`a` is first term and
`r` is the common ratio.

First term here is
`a=10x^3` and
`r` could be found by doing second term divided by first term,
`(40x^8)/(10x^3)=4x^5`.

Therefore the
`n`th term is given by

`a_n=10x^3 \cdot (4x^5)^(n-1)`.

So the
`7`th term is given by

`a_7=10x^3 \cdot (4x^5)^(7-1)`.

Let's simplify:

`a_7=10x^3 \cdot (4x^5)^(7-1)`

`a_7=10x^3 \cdot (4x^5)^(6)`

`a_7=10x^3 \cdot (4^6(x^5)^6)`

`a_7=10x^3 \cdot (4096x^30)`

`a_7=40960x^(33)`