Question

Find the sum of the given AP
=> 7+ 10 1/2 + 14+ ...........84

Answer 1

Clearly it is an A.P.

Here, a=7 ,d=7/2 , an=84 , Sn=?

We know that,
S = n/2 (a+l)
S = 23/2 (7+84)
S = (23/2) * 91
S = 2093/2
= 1046.5


So, the sum of 7+21/2+14+.............+84 is 1046.5

Answer 2

a= 7
d=21/2-7=7/2
Now, An= 84
or, a+(n-1)d=84
or, 7+(n-1)7/2=84
or, 7+7n/2-7/2=84
or, 14+7n-7=168 (by taking LCM
or, 7n=161
or, n= 23
then, Sn= n/2(a+l)
=23/2(7+84)
=23/2×91
=2093/2
=1046.5