Question

Evaluate 1+2+3+........+100.using this value find 7+14+21+.......+700.

Answer 1

Given,
1+2+3....100
a=1 a2=2
d=a2-a
=2-1
=1
w.k.t
Sn =n/2{2a+(n-1)d}
S100=100/2{2(1)+(100-1)1
=50{2+99}
=50{101}
=5050




7+14+21.........+70
a=7,a2=14
d=a-a2
=14-7
=7
Sn=n/2{2a+(n-1)d}
n=100
S100=100/2{2(7)+(100-1)7}
S100=50{14+(99)7}
S100=50{14+693}
S100=50{707}
S100=35350


OR
S100=5050
7(S100)=7×5050
=35350