Question

find the sum of sum of 16 successive odd numbers starting from 1 without actual addition

Answer 1

using AP sum formula,

Sn= n/2{2a+(n-1)d}

here n=16
a=1
d=2

Sn= 16/2{2x1+(16-1)2}

Sn= 8{2+30}
Sn= 8x32
Sn=256

Answer 2

Let AP be 1 , 3 , 5 ..........upto 16 terms

first term = 1 nd c.d=2 nd n=16

Sn=n/2[2a+(n-1)d]

S16=16/2[2×1+(16-1)2]

⇒8[2+15×2]

⇒8[2+30]

⇒8×32

⇒256

Hence, the sum of sum of 16 successive odd numbers starting from 1 is 256

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