Question

Write the next three terms in each of the gp,s 2,6

Answer 1

Answer:

The given GP would be

2, 6, 18, 54, 162, ...

Step-by-step explanation:

Given terms are

2,6...

since its in GP, we can calculate the common ratio (r) of the series

let denote

a = 2 and $a_{2} = 6 </em></p><p><em>r = [tex]\frac{a_{2} }{a_{1} } = \frac{6}{2} = 3$

As we know tht $n^{th}$ term of the GP is

$a_{n} = ar^{n-1}$ ........................................... (1)

to calculate the 3,4 and 5th term of GP,

let n =3 , n= 4 and n=5 respectively in equation (1)

$a_{3} = 2 * 3^{2} = 18\\  a_{4} = 2 * 3^{3} = 54\\a_{5} = 2 * 3^{4} = 162$

Hence the next three terms are

18 54 and 162

Happy to help