Find the common ratio for the geometric sequence.
-$\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \frac { 1024 } { 3 } , \ldots$
A) $\frac { 4 } { 3 }$
B) 4
C) 10
D) not geometric

Question

Quizplus · Accepted Answer

The common ratio in a geometric sequence is found by dividing any term by the previous term. For this sequence, dividing the second term ($\frac{16}{3}$) by the first term ($\frac{4}{3}$) gives $\frac{\frac{16}{3}}{\frac{4}{3}} = 4$. This ratio is consistent for all subsequent terms, confirming the sequence is geometric with a common ratio of 4.

Find the Common Ratio for the Geometric Sequence 43,163,643,2563,10243,…\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \frac { 1024 } { 3 } , \ldots34​,316​,364​,3256​,31024​,…

Find the Common Ratio for the Geometric Sequence $\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \frac { 1024 } { 3 } , \ldots$