If {Sₙ} = nP + frac{1}{2}n(n - 1)Q , where {Sₙ} denotes sum of first n terms of an A.P. , then c

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8. Sequences and Series

easy

If ${S_n} = nP + \frac{1}{2}n(n - 1)Q$, where ${S_n}$ denotes the sum of the first $n$ terms of an $A.P.$, then the common difference is

A

$P + Q$

B

$2P + 3Q$

C

$2Q$

D

$Q$

Solution

(d) Obviously ${S_n} = \frac{n}{2}\{ 2P + (n – 1)Q\} $, hence $d = Q$.

Aliter : $d = {T_2} – {T_1}$ $ = ({S_2} – {S_1}) – {S_1}$

$ = {S_2} – 2{S_1} = 2P + Q – 2P = Q.$

Standard 11

Mathematics

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