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!.