<h3><u>Question:</u></h3>
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?
<h3><u>Answer:</u></h3>
The first three terms of sequence is 9, 3 , 1
The common ratio is
<h3><u>Solution:</u></h3>
The geometric sequence is defined by the equation:
To find the first three terms of sequence, substitute n = 1, n = 2, n = 3
<em><u>First term:</u></em>
Put n = 1 in given equation
Thus first term of sequence is 9
<em><u>Second term:</u></em>
Put n = 2 in given equation
Thus second term of sequence is 3
<em><u>Third term:</u></em>
Put n = 3 in given sequence
Thus third term of sequence is 1
Thus the first three terms of sequence is 9, 3 , 1
<em><u>To find common ratio:</u></em>
Common ratio is found by dividing the two consecutive terms
Thus common ratio is obtained as:
Thus common ratio is