Question

How do I write a rule for the n-th term in this geometric sequence and then find a6?5,15,45,135

Answer 1

Given the sequence: 5,15,45,135

In general, the sequence for the n-th term is given by:

`a_n=a_1\cdot r^(n-1)`

Where:

r = common ratio

a1 = first term

Therefore:

`\begin{gathered} a_1=5 \\ r=(15)/(5)=3 \end{gathered}`

And we find a6:

Substitute a1 and r in the formula

`a_6=5\cdot3^(6-1)=5\cdot3^5=5\cdot243=1215`

Answer: a6 = 1215