Find the sum of 20 terms of the series

1² - 2² + 3² - 4² + 5² - 6² + ........ 20 terms.

 thanks loadzz rahul...!! =)

Always there

Good work harshita from my side

thank u harshita..!! =)

use a² - b² = (a + b)(a - b)

so, 1² - 2² + 3² - 4² + 5² - 6² + ................ + 19² - 20²

= (1 + 2)(1 - 2) + (3 - 4)(3 + 4) + (5 - 6)(5 + 6) + ...... + (19 - 20)(19 + 20)

= -3 -7 -11 - ..................... -39

= - [3 + 7 + 11 + ......... + 39]

a = 3 , d = 4 , l = 39

let thre be n terms in this A.P

so, 3 + (n - 1)(4) = 39

=> 3 + 4n - 4 = 39

=> 4n - 1 = 39

=> 4n = 40

=> n = 10

Thus, S = n/2 [a + l] = 10/2 [3 + 39] = 5 (42) = 210

Hence, S = -210 Ans...