Question

Which of the following is not a geometric progression?
A.1,2,4,8,16,32
B.4, - 4,4, - 4,4
C.12,24,36,48
D.6,12,24,48

Answer 1

In the given question we have to check in each and every option that whether there is a common ratio between the terms or not, because as we know that geometric series is formed when there is a common ratio between the first and second term, second and third term and so. For Example in the series 2,4,8,16,32 there is a common ratio i.e. 2. Now we have to apply this concept in the given problem as well. Thus we get the right answer.

Complete step-by-step answer:
For geometric progression, the ratio of the consecutive terms should be equal.
Let us check with the given options.
From the first option 1,2,4,8,16,32
This is a geometric progression because here the common ratio is 2. Here the given sequence is a geometric progression.
From the second option 4, - 4,4, - 4,4
This is a geometric progression because here the common ratio is - 1. Here the given sequence is a geometric progression.
From the third option 12,24,36,48
This is not a geometric progression because here only the difference is common i.e. 12. Here the given sequence is not a geometric progression.
From the fourth option 6,12,24,48
This is a geometric progression because here the common ratio is 2. Here the given sequence is a geometric progression.
Hence the correct answer is option C.

Note: In the given problem first we have to remember the concept of geometric progression, which is already given in the solution hint. Then we will apply this concept on the given options one by one, to check whether there is a common ratio between them or not. Hence we have seen that except option c all given series has a common ratio between them. Thus we will get the correct answer.