Question

The first term of a geometric sequence is 40, and the common ratio is 0.5. What is the 5th term of the sequence?

Answer 1

`T_5 = 2.5`

Explanation:

The `n^(th)` term of a geometric progression can be determined by using the formula:

`color(blue)(T_n = ar^(n-1))`
where: a = first term and r = common ratio

Substitute the given values of first term and common ratio into the formula:

`T_n = ar^(n-1)`
`T_5 = (40)(0.5)^(5-1)`
`T_5 = (40)(0.5)^(4)`
`T_5 = (40)(0.0625)`
`T_5 = 2.5`