Question

Identify the 17th term of a geometric sequence where a1 = 16 and a5 = 150.06. Round the common ratio and 17th term to the nearest hundredth.

Answer 1

GIVEN\( : \)
Your sequence is geometric, [and]
\(\color{#000000 }{ \displaystyle a_1=16 }\) (the first term of the sequence)
\(\color{#000000 }{ \displaystyle a_5=150.06 }\) (the 5th term of the sequence)

Answer 2

\(\color{#000000 }{ \displaystyle a_n=a_1\times r^{n-1} }\)
is all you need to know

Answer 3

\(\color{#000000 }{ \displaystyle a_n=a_1\times r^{n-1} }\)
\(\color{#000000 }{ \displaystyle a_5=a_1\times r^{5-1} }\)
\(\color{#000000 }{ \displaystyle 150.06=16\times r^{5-1} }\)

solve for r.

Answer 4

Then, apply \(\color{#000000 }{ \displaystyle a_n=a_1\times r^{n-1} }\) again.

\(\color{#000000 }{ \displaystyle a_n=a_1\times r^{n-1} }\)
\(\color{#000000 }{ \displaystyle a_{17}=a_1\times r^{17-1} }\)

And once you solved for r, and you were given \(a_1\)....