Question

the number of bacteria in a certain food item after each second,when double in every second.Is that an AP?Why?

Answer 1

No, they are not in AP...

If there are x bacteria now,

there will be 2x after a second

and, 4x after 2 sec.


Sequence ---> x, 2x, 4x, .......


Thus, there is no common difference. So, it's not an AP.

Instead it is in GP...

Answer 2

Given : The number of bacteria in a certain food item after each second forms an A.P.  When they double in every second

To Find :  True or False  , Is that an AP? Why?

Solution:

Let say in beginning Bacteria

A

After 1 sec  = 2A

After 2 sec  = 4A

After 3 Sec = 8A

Bacterial

A  , 2A  , 4A  , 8A

AP has common difference between consecutive terms

2A - A = A

4A - 2A  = 2A

8A - 4A  = 4A

But here difference is not common

Hence This does not form an AP

This is an GP with common Ratio = 2

2A/A = 4A/2A  = 8A/4A = 2

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