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

Jun 2, 2018

$118098$ is the ${11}^{t h} t e r m .$

#### Explanation:

We know that,

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

color(blue)(a_n=a_1(r)^(n-1)

$w h e r e , {a}_{1}$ is first term and $r$ is common ratio.

Here,

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

So,

${a}_{1} = 2 , r = \frac{6}{2} = 3 , \mathmr{and} {a}_{n} = 118098$

$\therefore {a}_{n} = 2 \cdot {\left(3\right)}^{n - 1} = 118098$

$\implies {3}^{n - 1} = \frac{118098}{2} = 59049$

$\implies {3}^{n - 1} = {3}^{10}$

$\implies n - 1 = 10$

$\implies n = 11$

Hence, $118098$ is the ${11}^{t h} t e r m .$