Ageometric sequence is defined by the equation an = (3)3 − n. what are the first three terms of the sequence and what is the common ratio, r?

Question:

A geometric sequence is defined by the equation an = (3)^3 − n. What are the first three terms of the sequence and what is the common ratio, r?

The first three terms of sequence is 9, 3 , 1

The common ratio is

Solution:

The geometric sequence is defined by the equation:

To find the first three terms of sequence, substitute n = 1, n = 2, n = 3

First term:

Put n = 1 in given equation

Thus first term of sequence is 9

Second term:

Put n = 2 in given equation

Thus second term of sequence is 3

Third term:

Put n = 3 in given sequence

Thus third term of sequence is 1

Thus the first three terms of sequence is 9, 3 , 1

To find common ratio:

Common ratio is found by dividing the two consecutive terms

Thus common ratio is obtained as:

Thus common ratio is

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Sry i’m so bad at math! wish i could answer #imdumb