Question

Say true or false. \[2,4,8,16...\] is not an A.P.

Answer 1

Hint:
The A.P. is Arithmetic Progression refers to a series of sequences in which the difference between the adjacent terms is constant throughout the series means the same difference and that difference is said to be the common difference that is the difference which is common over the series. As we are given series \[2,4,8,16...\] when we find the difference between all the adjacent terms if that is the same means the series is an A.P. otherwise not. So in this series the difference between the first two terms and the difference between the next two terms is not the same hence the series is not in an A.P.

Complete step by step solution:
We are given as series,
\[2,4,8,16...\]
Now to check whether it is an A.P. or not we would the calculate the difference between the terms
\[\Rightarrow \] Difference between first two terms is \[4-2=2\]
\[\Rightarrow \] Difference between next two terms is \[8-4=4\]
Since the difference is not same between the adjacent terms
Therefore, we can say that the given series is not an A.P.

Hence, the answer is True.

Note:
When we have to check whether a series is in an A.P. or not just check the difference between the adjacent terms if this is the same then the series would be in A.P. otherwise not. In an A.P. series we can calculate any term by just knowing the common difference and one of its terms.