Question

What are the next three terms of the following sequence?

8, 40, 200, 1000

What are the next three terms of the following sequence?
-10, 20, -40, 80

What are the next three terms of the following sequence?
-2, 4, -8, 16

Answer 1

we know that given terms were i geometric progression.

which means common ratio is same between two consecutive terms .

here we have 8,40,200,1000.

we know that common ratio =second term/first term =40/8=5.

so each and every terms is multiplied by 5 to get next term for this series the term after 1000 is 5000 =1000*5.

in part b we have another series which is having common ratio of -2.

so we need to multiply with -2 to find next term.

80*(-2)=-160.

for part c the common ratio is -2 .

so we need to multiply with -2 *previous term =-2*16 =-32.

Answer 2

We can see first sequence :

40/8 = 5

200/40 = 5

1000/200 = 5

this implies it is a geometric sequence with common ratio r= 5 and first term a= 8

every next term can be achieved by multiplying 5 to previous term

5th term = 1000 * 5 = 5000

6th term = 5000 * 5 = 25000

7th term = 25000 * 5 = 125000

LEt us work on next one : 20/-10 = -2 , -40/20 = -2 80/-40 = -2

5th term : 80 *(-2) = -160

6th term : -160* -2 = 320

7th term = 320*-2 = -640

next is : 4/-2 = -2 -8/4 = -2 16/-8 = -2

5th term = 16 *- 2= -32

6th term = - 32*-2 = 64

7th term = 64*-2 = -128