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:

$\begin{gathered} a_1=5 \\ r=\frac{15}{5}=3 \end{gathered}$

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