Question

Find the 13th term of the geometric sequence

3
,
−
15
,
75
,
.
.
.
3,−15,75,...

Answer 1

The
`13^(th)` term of the geometric sequence is - 732421875.

A geometric sequence is given ; 3 , -15 , 75....

We have to find the
`13^(th)` term of the geometric sequence.

What is the formula for calculation of nth term of geometric Sequence ?

The formula for calculation of nth term of geometric progression is
`a_(1) =a^(n) x (r)^(n-1)`where r is the common ratio of geometric sequence.

Given geometric sequence is 3 , -15 , 75....

and

Common ratio is r.

i.e., r = -15 ÷ 3 = -5

∵
`{n}^t^h` term of a geometric sequence is given by ;

`a_(1) =a^(n) x (r)^(n-1)`

where is the first term.

Hence,

`13^(th)` term of the geometric sequence will be ;

`a_(13)=3x(-5)^1^2`

`a^1^3` = - 732421875

Thus , the term of the geometric sequence is - 732421875.