Q. 84.2( 22 Votes )

Two APs have the same common difference. The first term of one of these is - 1 and that of the other is - 8. The difference between their 4th terms is?

Answer :

Given: a = - 1


A = - 8


To find: a4 -A4


Formula Used: nth term of an AP is:


an = a + (n - 1) d


Explanation:


Let a and A be the first terms of Two AP’s.


a = - 1


A = - 8


Let d and D be the common differences of two AP’s.


D = d ……. (i)


Let a4 and A4 be the 4th terms of two AP’s.


As we know, nth term of an AP is


an = a + (n - 1) d


where a = first term


an is nth term


d is the common difference


a4 -A4 = a + 3d – (A + 3D)


= a + 3d - A - 3d (using ( i ) )


= a - A


= - 1 - (- 8)


= -1 + 8


= 7


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