Sum of n terms of three different arithmetic progressions are S,. S S,

1.	Sum of n terms of three different arithmetic progressions are S,. S S, If first temmall three A.Ps is 1 and their common differences are 1. 2 and 3 respectively, then provethat S, +S2S2are S. S, S,. If first term of
Answer» s1= [2a +(n-1)d]n/2 =[2a +n-1)n/2 s2=[2a+(n-1)2]n/2 =[2a+2n-2]n/2 =(2an +2n^2-2n)/2 s3=[2a+(n-1)3]n/2 =(2a+3n-3)n/2 s3+s1=[2an+3n^2-3n +2an+n^2-n]/2 =(4an+4n^2-4n)/2 =2an+2n2 -2=2s2

Sum of n terms of three different arithmetic progressions are S,. S S, If first temmall three A.Ps is 1 and their common differences are 1. 2 and 3 respectively, then provethat S, +S2S2are S. S, S,. If first term of

Answer»

s1= [2a +(n-1)d]n/2

=[2a +n-1)n/2

s2=[2a+(n-1)2]n/2

=[2a+2n-2]n/2 =(2an +2n^2-2n)/2

s3=[2a+(n-1)3]n/2 =(2a+3n-3)n/2

s3+s1=[2an+3n^2-3n +2an+n^2-n]/2

=(4an+4n^2-4n)/2

=2an+2n2 -2=2s2