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

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

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.