Question

find the sum of (40^2-39^2)+(38^2-37^2)+(36^2-35^2)+.............+ (2^2-1^2)
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Answer 1

(40²-39²)+(38²-37²)+(36²-35²)+.......+(2²-1²)

(1600-1521)+(1444-1369)+(1296-1225)+.....+(4-1)

79+75+71+.......+(3)

a1= 79 ,a2=75

d =a2-a1= 75-79 = -4

an=3

an= a+(n-1)d

3 = 79 + (n-1)(-4)

3-79 =(n-1)(-4)

-76=(n-1)(-4)

-76/-4= n-1

19=n-1

n=20

we know

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

S20= 20/2[2×79+(20-1)(-4)]

= 10[158-76]

= 10[82]

=820