Question

Each term of an AP whose first term is a and common difference d is doubled .Is the resulting sequence an AP? If no find its first term and cd

Answer 1

The general form of an AP is  a,  a+d, a+2d,.....

where a is the first term and d is the common difference  

If we double the terms,  the new sequence would be

A , a+2d, a+4d,......

We can observe that this sequence is also an AP

First term is a

Common difference is 2d  nth term= 2a+(n-1)2d               = 2[a+(n-1)d]

Answer 2

when first term = a
and common difference = d
then AP series is a, a+d, a+2d,.....

when it doubles 2a, 2(a+d),2(a+2d).....
then first term =2a
and common difference = 2d