Question

Find an explicit formula for the geometric sequence -1,-7,-49,-343,.... Note : the first term should be d(1) . d(n) =

Answer 1

Given:

The geometric sequence is

`-1,-7,-49,-343,...`

To find:

The explicit formula for the given geometric sequence.

Solution:

We have,

`-1,-7,-49,-343,...`

Here, the first term is -1 and the common ratio is

`r=(-7)/(-1)`

`r=7`

The explicate formula of a geometric sequence is

`a_n=ar^(n-1)`

Where, a is the first terms and r is the common ratio.

The first terms is d(1)=-1 and the common ratio is 7. So, the explicit formula is

`d(n)=d(1)(7)^(n-1)`

`d(n)=-1(7)^(n-1)`

`d(n)=-(7)^(n-1)`

Therefore, the explicit formula for the given geometric sequence is
`d(n)=-(7)^(n-1)`.