Question

If the fifth term in a geometric sequence is 1∕27 and the common ratio is 1∕3, find the explicit formula of the sequence.

Answer 1

Answer:

Explicit formula will be $A_n=3^{(2-n)}$

Step-by-step explanation:

Explicit formula for a geometric sequence is given by the formula,

$A_n=a(r)^{n-1}$

Here $A_n$ is the nth term of the sequence

a = first term of the sequence

n = number of term

Since 5th term of a geometric sequence is

$A_5$ = $\frac{1}{27}$

First term of the sequence 'a'= $\frac{1}{3}$

By substituting these values in the explicit formula,

$\frac{1}{27}=a(\frac{1}{3})^{5-1}$

$\frac{1}{27} =a(\frac{1}{3})^4$

a = $\frac{\frac{1}{27}}{\frac{1}{81}}$

a = $\frac{81}{27}$

a = 3

Therefore, explicit formula of this sequence will be,

$A_n=(3)(\frac{1}{3})^{n-1}$

$A_n=(3)(3)^{(-n+1)}$

$A_n=3^{(2-n)}$