Question

find the sum of AP 1^2-2^2+3^2-4^2+..... upto 50 terms

Answer 1

answer is in picture

hope this is helpful

Answer 2

Answer:

The sum of AP is -1275

Step-by-step explanation:

Given : AP $1^2-2^2+3^2-4^2+.....$  upto 50 terms.

To find : The sum of AP

Solution :

We can write the series as,

$1^2-2^2+3^2-4^2+.....+49^2-50^2$

$(1^2+3^2+5^2+.....+49^2)-2^2(1^2+2^2+3^2+.....+25^2)$

Applying the series formula,

$1^2+3^2+5^2+.....+49^2=\frac{n(2n+1)(2n-1)}{3}$

$-2^2(1^2+2^2+3^2+.....+25^2=-2^2(\frac{n(n+1)(2n+1)}{6})$

Substitute,

$=(\frac{25(51)(49)}{3})-4\frac{25(26)(51)}{6})$

$=\frac{25(51)}{3}(49-52)$

$=\frac{25(51)}{3}(-3)$

$=-1275$

Therefore, The sum of AP is -1275.