Question

Write a rule for a geometric sequence that has a 1 as its first term and a common ratio of -4. what is the seventh term of this sequence

Answer 1

I hope first term is 1.

Hope this is your question, if not I think you will, still be able to

find an answer of your question based on this solution.

The formula for general term of a geometric sequence is,

`a_(n) =a_(1) *r^(n-1)`

Where, first term: a_{1} =1 and common ratio: r = -4.

So, first step is to plug in the values of a1 and r in the above formula to get the rule of this geometric sequence. Hence,

`a_(n) =1 *4^(n-1)`

`a_(n) =4^(n-1)`

So, the rule of the geometric sequence is
`a_(n) =4^(n-1)`.

To find the seventh term, plug in n = 7 in the above rule. Therefore,

`a_(7) =4^(7-1)`

=
`4^6`

= 4096

Hope this helps you!.