Question

What is the next term in the geometric sequence 4
-16, 64,.....?​

Answer 1

Answer:

4 -16 64 -256

Step-by-step explanation:

4(-4) = -16

-16 (-4)= 64

64 (-4) = -256

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Answer 2

Answer:

The next term would be -256.

Given :

Given series is 4 , -16 , 64

To Find :

Find the next term.

Step-by-step explanation:

Following series is the example of geometric progression.

Geometric progression. : In mathematics, such a series of numbers is called a geometric series, in which the ratio of any two consecutive terms is constant. Each term of G.P. is obtained by multiplying a fixed non-zero number in the previous term. This fixed number is called the 'common ratio'. For example 2, 6, 18, 54, .

Common Ratio (r) :

common ratio is the ratio of the two consecutive terms.

Given series is 4 , -16 , 64

First term   , a = 4

Common ratio (r) = -16/4

r= -4

nth term of the geometric progression Tₙ=  $ar^{n-1}$

So the fourth term , T₄ = $4.(-4)^{4-1}$

                                     =4x(-4)³

                                     =4x(-64)

                                     =-256

Hence the next term would be -256.