Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
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Question

Quizplus · Accepted Answer

The fifth term of a geometric sequence with initial term $a$ and common ratio $r$ is $ar^4$ (since we are finding the 5th term, which is 4 terms after the first term). 
The nth term of a geometric sequence with initial term $a$ and common ratio $r$ is $ar^{n-1}$.

Therefore, the fifth term is $a r^4$, and the nth term is $ar^{n-1}$.

Using the values given in the question: 
a = 11ebbed0_ca32_4836_8acb_3fe1f68b6fd7_TB8253_11 
r = TB8253_11

The fifth term is $(11ebbed0\_ca32\_4836\_8acb\_3fe1f68b6fd7\_TB8253\_11)(TB8253_{11})^4 = 11ebbed0\_ca32\_4837\_8acb\_996a56944647\_TB8253\_11$

The nth term is $(11ebbed0\_ca32\_4836\_8acb\_3fe1f68b6fd7\_TB8253\_11)(TB8253_{11})^{n-1}$

Find the Fifth Term and the Nth Term of the Geometric