Question

7, -21, 63, .. Find the 15th term of the geometric sequence

Answer 1

Geometric Sequence :

Every term in a geometric sequence is obtained by multiplying the term before it by the same number.  $A_{n}$ = $a_{}$ $r^{n-1}$ is the general term for it. The common ratio is denoted by the number 'r'. Any term in the sequence can be used to find it by dividing it by the term before it.

'a' is the first term of the sequence, n is the  $n^{th}$ term.

Given geometric sequence :

7 , -21 , 63 , ....

Here, first term = a = 7

common ratio = r = $\frac{-21}{7}$ = -3

n = 15.

Then, $15^{th}$ term =  $A_{15}$ = 7 x $(-3)^{15-1}$

                                    = 7 x $(-3)^{14}$  =  7 x 4,782,969

                                    = 33,480,783 .

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