Question

4. In the series 2, 6, 18, 54, ..... what will
be the 8th term? ans​

Answer 1

Working out:

Given a sequence and we are asked to find the nth term of this GP. We can observe that the successive terms are multiplied by 3 previous term.

• So it is a Geometric progression.

It is sequence of non-zero (Imp.) numbers in which the ratio of a term and the term preceding is always a constant. This is known as constant ratio r.

GiveN:

• Sequence = 2,6,18,54.....

and we are asked to find the 8th term of the GP?

Here, nth term is 8th term. This can be solved by using the formula for finding nth term i.e.

$\large{ \boxed{ \sf{an = a {r}^{n - 1} }}}$

And,

• a = first term = 2
• r = common ratio = 6/2 = 18/6 = 3
• n = 8

Plug in the values to the result,

$\sf{ \longrightarrow{a8 = 2{(3)}^{8 - 1} }}$

$\sf{ \longrightarrow{a8 = 2(3) {}^{7} }}$

$\sf{ \longrightarrow{a8 = 2 \times ( {3}^{4} \times {3}^{3} )}}$

$\sf{ \longrightarrow{a8 = 2 \times (81 \times 27)}}$

$\sf{ \longrightarrow{a8 = 2 \times 2187}}$

$\sf{ \longrightarrow{a8 = 4374}}$

Hence, the 8th term of the GP is:

$\huge{ \boxed{ \sf{ \red{4374}}}}$

And we are done !!