Question

PLEASE HELP I REALLY NEED IT! Write an equation for the nth term of the geometric sequence 5,15,45,135,405,…

Then find a8

Answer 1

An equation to represent the given geometric sequence would be
`a(x)=5*3^(x-1)`, and a(8) of the geometric sequence will be 10,935.

Explanation:

In order to write an equation for a geometric sequence, first we must analyze the sequence to find its starting value and its constant ratio. The starting value is simply the first term in the sequence, which is 5. As for the constant ratio, it is the rate of change that the equation uses. In this sequence, the constant ratio is 3. Now, we can write out an equation for this geometric sequence.

We know the first term of the sequence is 5, and the common ratio is 3, so we can write out a function for the geometric sequence, which will be
`a(n)=5*3^(n-1)`. NOTE that the exponential power is n - 1, and not n. This is because the first term of the sequence is 5, and not the "0th" term, therefore we must subtract 1 from n (the term number) to have the right sequence.

Lastly, we can use the equation
`a(n)=5*3^(n-1)` to find the 8th term of the sequence by replacing n with 8. So
`a(x)=5*3^(n-1)` would become
`a(8)=5*3^(8-1)`, and you will get
`a(8)=5*3^(8-1)` ⇒
`a(8)=5*3^(7)` ⇒
`a(8)=5*2187` ⇒
`a(8)=10,935`. Therefore, the equation for the nth term of the geometric sequence would be
`a(n)=5*3^(n-1)`, and the 8th term of the sequence is 10,935.

Have a great day! Feel free to let me know if you have any more questions :)