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

User Oezguensi
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1 Answer

2 votes

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).

User Olivejp
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