Which term of the geometric sequence 2,6,18 is 118,098?

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Answer 1 · 2018-06-02T04:54:04

$118098$ $118098$ is the $11^{t h} t e r m .$ $11^(th) term.$

We know that,

$n^{t h} t e r m$ $n^(th) term$ of geometric seqn. is:

$a_{n} = a_{1} {(r)}^{n - 1}$ $color(blue)(a_n=a_1(r)^(n-1)$

$w h e r e, a_{1}$ $where, a_1$ is first term and $r$ $r$ is common ratio.

Here,

Geometric Sequence: $2,6,18,...,118098.$

So,

$a_1=2 , r=6/2=3, and a_n=118098$

$:.a_n=2*(3)^(n-1)=118098$

$=>3^(n-1)=118098/2=59049$

$=>3^(n-1)=3^10$

$=>n-1=10$

$=>n=11$

Hence, $118098$ is the $11^(th) term.$