The sum 1^2-2.3^2+3.5^2-4.7^2+5.9^2- +15.29^2 is ........ - Vidyadip

MCQ

The sum $1^2-2.3^2+3.5^2-4.7^2+5.9^2-\ldots +15.29^2$ is $.......$.

A
$6950$
B
$6956$
C
$6953$
✓
$6952$

✓

Answer

Correct option: D.

$6952$

d
Separating odd placed and even placed terms we get

$S =\left(1 \cdot 1^2+3 \cdot 5^2+\ldots .15 \cdot(29)^2\right)-\left(2 \cdot 3^2+4.7^2\right.+\ldots .+14 \cdot(27)^2$

$S =\sum \limits_{ n =1}^8(2 n -1)(4 n -3)^2-\sum_{ n =1}^7(2 n )(4 n -1)^2$

Applying summation formula we get

$=29856-22904=6952$

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