Q. 24

# The common difference of an A.P., the sum of whose n terms is S_{n}, is

A. S_{n} – 2S_{n–1} + S_{n–2}

B. S_{n} – 2S_{n–1}– S_{n–2}

C. S_{n} – S_{n–2}

D. S_{n} – S_{n–1}

Answer :

a_{n} is the n^{th} term of an A.P and a _{n–1} is the (n–1)^{th} term of an A.P,

d = common difference, S_{n} = sum of n terms of an A.P

d= a_{n} – a_{n–1}

But a_{n}= S_{n} – S_{n–1}

And a_{n–1}= S_{n–1} – S_{n–2}

So d= S_{n} – S_{n–1} – (S_{n–1} – S_{n–2})

d= S_{n} – 2 S_{n–1} + S_{n–2}

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