Question

Find the sum to 100 terms of the series 1 + 4 + 7 + 5 + 13 + 6

Answer 1

given:-
a= 1
d= a2-a1 = 4 - 1 = 3
n = 100
to find:-
s100
solution:-
sn= n/2 ( 2a+( n-1)d)
s100 = 100/2 ( 2×1 + (100-1) 3 )
= 50 ( 2+ 99×3)
= 50 ( 2+297)
= 50×299
s100 = 14950

Answer 2

Step-by-step explanation:

The series can be clubbed into two Ap's,(1+7+13....) and (4+5+6...). So we can observe that the series can be taken as two AP's. Now, we can find sum of 50 terms of each ap formed.

Formula for sum of first n terms of AP is

Sn=n/2(2a+(n-1)d)

so for first AP

S1=50/2(2+(50-1)×6)=7400

similarly,

S2=50/2(8+(50-1)×1)=1425

So, sum of first 100 terms =7400+1425=8825