Question

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. {5,5/3,5/9

Answer 1

The general term of the given sequence is given by: $5(\frac{1}{3}) ^{n-1}$

What is a Geometric Progression and what is its General Term?

Geometric progression refers to a special progression, or a sequence of numbers, in which each successive term is a fixed multiple of the term preceding it.

For a geometric progression having first term 'a', a constant ratio of the terms be 'r' and 'n' number of terms, then:

General Term of Geometric Progression(G.P.) = $ar^{n-1}$, where r > 0.

Given: $5,\frac{5}{3},\frac{5}{9},...$

Here, for the given G.P., a = 5, r = $\frac{1}{3}$

Then, the general term = $5(\frac{1}{3}) ^{n-1}$, if the given G.P. has 'n' terms.

To learn more about geometric progressions, refer to the link: brainly.com/question/1509142

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