Question

(1 point) Find a formula for the nth term in the sequence: 17,−17/8,17/27,−17/64,17/125,…

Answer 1

Given:

The sequence is:

`17,-(17)/(8),(17)/(27),-(17)/(64),(17)/(125),...`

To find:

The formula for the nth term in the given sequence.

Solution:

We have,

`17,-(17)/(8),(17)/(27),-(17)/(64),(17)/(125),...`

The given sequence can be written as

`(17)/(1^3),-(17)/(2^3),(17)/(3^3),-(17)/(4^3),(17)/(5^3),...`

The sign are alternative and the absolute value of each term can be defined by the expression
`(17)/(n^3)`, where n is a natural number.

So, the required formula is:

`a_n=(-1)^(n+1)(17)/(n^3)`

Therefore, the formula for nth term in the given sequence is
`a_n=(-1)^(n+1)(17)/(n^3)`.