337S= 1 + (- 4 + 9) + (- 16 + 25) + (- 36 + 49) ... n
→ S= 1 + 5 + 9 + 13 ... n
a1= 1.
d=4.
So, ans= (2*a1 + (n-1) d) n2
= (2n-1) n.
Sayantan Hazra Simple check : Put n = 2...... :)Upvote·0· Reply ·2013-07-15 12:43:45
If S = 1 - 22 + 32 - 42 upto n terms and n is even, then find S.
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2 Answers
337337S= a1 - a2 + ... an
→ S= a1 + (-a2 + a3)... +(-an-2+ an-1) +an.
Our series is (-a2 + a3)... +(-an-2+ an-1)
This series has (n-2)/2 terms.
So, formula gives answer, (2*5 + (((n-2)/2)-1 )* 4)n-24
= (7-n) (n-2)2
Now, we have to add the first and last terms.
So final answer = 1 + (7-n) (n-2)2 + nth term...
- Sayantan Hazra Check : Put n = 4 ........ :)
- Sayan Sinha This one works when n is odd.