Question

Find which of the following are not G.P.a. 6, 12, 24, 48, ..... b. 1, 4, 9, 16, ......c. 1, −1, 1, −1, ..... d. −4, −20, −100, −500, .....

Answer 1

Hey there!
Geometric progression is a series in which the consecutive terms have a constant ratio .

a. 6 , 12 , 24 , 48 , . . . . . .
b. 1 , 4 , 9 , 16 , . . . . .
c. 1 , -1 , 1 , -1 . . . . .
d . -4 , -20 , -100 , -500 . . . . . . .

a) 6 , 12 , 24 , 48
12/6 = 2
24/12 = 2
48/ 24 = 2

There is a common ratio between the terms of the series, Hence it is a G . P.

b) 1 , 4 , 9 , 16 , . . . . . . . . .
4/1 = 4
9/4 = 9/4
16/9 = 16/9

There is no common ratio between the terms of series, therefore it is not a Geometric progression.

c) 1 , -1 , 1 , -1 , . . . . . . .

-1/1 = -1
1/-1 = -1
-1/1 = -1

There is a common ratio between the terms of the series, Hence it is a G . P.

d ) -4 , -20 , -100 , -500 , . . . . . . .

-20/-4 = 5
-100/-20 = 5
-500/-100 = 5 .

There is a common ratio between the terms of the series, Hence it is a G . P.

Hope helped!