Question

Find the nth term of G.P 8,24,72,216.........

Answer 1

The nth of the GP would be 8/3 3^n

Given

• G.P 8,24,72,216

To find

• the nth term of G.P

Solution

we are provided with a geometric progression and her asked a to find the end the term of the geometric progression.

The n the term of the geometric progression could be estimated by using the first term as well as the common ratio of the GP and substitute it in this standard equation to find the nth the term.

first term of the geometric progression,a = 8

common ratio = 24/8

or, r = 3

the nth the term of the GP is given by,

an = a× r^(n-1)

or, an = 8 × 3^(n-1)

or, an = 8× 3^n × 3^(-1)

or, an = 8/3 3^n

Therefore, the nth of the GP would be 8/3 3^n

Answer 2

According to the question;

G.P :- 8, 24, 72, 216, ..........

First-term (a) = 8

Common ratio (r) = $\frac{24}{8}$

or r = 3

$a_{n} = a(r)^{n-1}$

= 8 × (3)ⁿ × (3)⁻¹

=$\frac{8}{3} *3^{n}$

The nth term of G.P 8,24,72,216......... is $\frac{8}{3} *3^{n}$.

• Geometric Progression (GP) is a type of sequence in which each succeeding term is produced by multiplying the previous term by a fixed number known as a common ratio.
• The common ratio is the common multiple between each successive term and the preceding term in a GP. It is a constant value that is multiplied by each term in the Geometric series to get the next term. If the first term is a and the second term is ar.

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