NCERT Class XI Mathematics - Sequences and Series - Solutions

Question : 22

Total: 106

If the sum of n terms of an A.P. is (pn+qn2), where p and q are constants, find the common difference.

Solution:

We have Sn = pn + qn2, where Sn be the sum of n terms.
S1 = p + q (sum of 1 term i.e., first term)
S2 = 2p + 4q (sum of 2 terms i.e., sum of first term & second term)
Also, S2 = a1+a2
∴ 2p + 4q = p + q + a2 ⇒ p + 3q = a2
Thus, common difference d = a2–a1 = p + 3q – p –q = 2q

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