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

Question

asked Apr 26, 2023 30.6k views

1 Answer

Kvam · Answer 1 · 2023-05-01T14:02:56+0000

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