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:

$17,-\dfrac{17}{8},\dfrac{17}{27},-\dfrac{17}{64},\dfrac{17}{125},...$

To find:

The formula for the nth term in the given sequence.

Solution:

We have,

$17,-\dfrac{17}{8},\dfrac{17}{27},-\dfrac{17}{64},\dfrac{17}{125},...$

The given sequence can be written as

$\dfrac{17}{1^3},-\dfrac{17}{2^3},\dfrac{17}{3^3},-\dfrac{17}{4^3},\dfrac{17}{5^3},...$

The sign are alternative and the absolute value of each term can be defined by the expression $\dfrac{17}{n^3}$, where n is a natural number.

So, the required formula is:

$a_n=(-1)^{n+1}\dfrac{17}{n^3}$

Therefore, the formula for nth term in the given sequence is $a_n=(-1)^{n+1}\dfrac{17}{n^3}$.