Question

If the first term in a geometric sequence is $3$, and if the third term is $48$, find the ${11}^{th}$ term.

• A. $228$
• B. $528$
• C. $110592$
• D. $3145728$
• E. $12582912$

Answer 1

Answer: (D)

$3145728$

In a geometric series $a_n=a\cdot r^{n-1}$ where $a_1$ is the first term of the sequence, $r$ is the common ratio and $n$ is the number of the term.

Then $a_3=48=3(r{)}^{4-1}$

$\Rightarrow 48=3(r{)}^2$

$\Rightarrow r=4$

Then $a_{11}=3(4{)}^{11-1}=3(4{)}^{10}=3\times 1048576=3145728$