Question

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 16,80, 400,... Find the 6th term.

Answer 1

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 16,80, 400,... Find the 6th term.​

we have

a1=16

a2=80

a3=400

so

a2/a1=80/16=5

a3/a2=400/80=5

In this problem we have a geometric sequence

where the common ratio is equal to r=5

the equation for the geometric sequence is equal to

$a_n=a_1\cdot(r)^{(n-1)}$

substitute the give values

$a_n=16\cdot(5)^{(n-1)}$

Find the 6th term

For n=6

substitute

$\begin{gathered} a_6=16\cdot(5)^{(6-1)} \\ a_6=16\cdot(5)^{(5)} \\ a_6=50,000 \end{gathered}$

therefore

the answer is 50,000