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Question: The sum of the series a – (a + d) + (a + 2d) – (a + 3d) + … (2n + 1) terms is...

The sum of the series

a – (a + d) + (a + 2d) – (a + 3d) + … (2n + 1) terms is

A

– nd

B

a + 2nd

C

a + nd

D

2nd

Answer

a + nd

Explanation

Solution

S = a – (a + d) + (a + 2d) – (a + 3d) +...(a + 2nd) ….(i)

This is A.G.P. series

(–1)S = – a + (a + d) – (a + 2d) + … – (a + 2nd) ….(ii)

(i) – (ii) :

2S = a + 0 + (a + 2nd)

S = a + nd