Two APs are considered with the same common . . .

Question : Two APs are considered with the same common difference. If the first term of an AP is 6 and of the other AP is (-5), then find the difference between their nth terms and hence between their 16th terms. 

Doubt by Zoha

Solution : 

Let the first term of first AP be A and first term of second AP is a and the common difference of both the AP be d. 

A=6

a=-5

For First AP 
An=A+(n-1)d
An=6+(n-1)d — (1)

For Second AP
an=a+(n-1)d
an=(-5)+(n-1)d
an=-5+(n-1)d — (2)

Subtracting equation (2) from equation (1)

An-an=6+(n-1)d-[-5+(n-1)d]
An-an=6+(n-1)d+5-(n-1)d
An-an=6+5
An-an=11

Similarly 

A6-a6

=A+(n-1)d-[a+(n-1)d]

=6+(6-1)d-[-5+(6-1)d]
=6+5d-[-5+5d]
=6+5d+5-5d
=11

Hence
A6-a6=11