Question

Without adding find the sum of 1+3+5+7+.......+23

Answer 1

a=1 ; d=3-1=5-3=2 ; l=23; n=23

Sn=n/2(a+l)

S23=23/2(1+23)

=23/2*24

=23*12=276.

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Answer 2

Hey sup!

As per the question,

a=1
d=3-1=2.
l=23.
A(n)=a+(n-1)d.
=>23=1+(n-1)2.
=>23-1=(n-1)2.
=>22/2=n-1.
=>11=n-1.
=>n=11+1=12.

S(n)=n/2(a+l)
S(12)=12/2(1+23).
S(12)=6*24.
=>S(12)=144.

The sum is 144.

Hope it helps.