Question

Without adding find the sum
(a) 1 + 3 + 5 + 7 + ..... + 23 = ?
(C) 1 + 3 + 5 + 7 + ..... + 39 = ?​

Answer 1

1?

an =a+(n-1)d=1+(n-1)2=23

2n-2=22

2n=24

n=12

S12=12/2×{2+22}=6×24=224

2?

an=1+(n-1)2=39

2n-2=38

2n=40

n=20

S20=20/2{2+38}=400

Answer 2

400 will be the sum.

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