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

the common ratio
\[r=a _{n}/a _{n-1}\]
\[ar ^{5-1}/ar ^{1-1}=r ^{4}\]
\[r^{4}=a _{5}/a _{1} =150,06/16=9,37875\]
\[r=1,749992711\]
\[a _{17}=ar ^{16}=16(1,749992711)^{16}=123794,064\]