Question

what is the next term in the geometric sequence -2, 6, -18,

(A) 54 (b) -54 (c) 9 (d) -9

Answer 1

Let the first term -2 be a and then,

Common ratio = any term / previous term

                        = - 18 / 6 = 6 / - 2

                        = - 3

Common ratio ( r ) = - 3

Three term are already given, so the next term should be the fourth term of the GP.

We know, in GP $a_{n} = ar^{n-1}$

So, assuming 4th term of the given GP as nth term according to the identity.

$a_{4} = ar^{4-1}$

$a_{4} = ar^{3}$

        Substituting values from the question :

$a_{4} = -2 \times ( - 3 )^{3}$

$a_{4} = -2 \times - 27$

$a_{4} = 54$

Therefore next term of the given GP is 54.