Question

Given a term in a geometric sequence and the common ratio, find the explicit formula, a11=5120 ans r=-2

Answer 1

`U_n=5(-2)^(n-1)`

Explanation:

Given a geometric sequence, the nth term of the geometric sequence is obtained by using the formula:

`U_n=ar^(n-1)`

If the eleventh term,
`a_(11)=5120`

and the common ratio, r=-2.

Then:

`5120=a(-2)^(11-1)\\a=(5120)/(2^(10)) =5`

The explicit formula for the sequence is:

`U_n=5(-2)^(n-1)`