Question
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