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Q.

If s1, s2, s3sq are the sums of n terms of q A.P.'s whose first terms are 1, 2, 3 ....q and common differences are 1,3,5, ..... (2q–1), respectively then s1+s2+s3++sq=
 

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a

nq 
 

b

 nq2

c

12nqnq-1

d

12nqnq+1

answer is A.

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Detailed Solution

S1=n22(1)+(n-1)1=n2n+1 S2=n22(2)+(n-1)3=n23n+1 S3=n22(3)+(n-1)5=n25n+1 sq=n22(q)+(n-1) (2q-1)=n22q-1n+1 S1+S2.....+Sq =n21+3+5....+(2q-1)n+q =n2nq2+q=nq2(nq+1)

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