Question

Find the sum of the first 40 terms of series 1²-2²+3²-4².....

Answer 1

given that AP is
-3 +(-7) + (-9) + (-11)
here a1 = -3 a2 = -7 a3 = -9 a4 = -11
d = a2-a1 = a4- a3 =
-7+3=-11+9
-4 = -2
there is no common diffrence

Answer 2

Answer:

Step-by-step explanation:

Here we can put a²-b² formula to get

(1²-2²)+(3²-4²)........

So we get a²-b²= (a+b)(a-b)

(1+2)(1-2)+(3-4)(3+4).........

notice that (1-2),(3-4),(4-5) all add up to -1 so by taking -1 common

-1(3+7+11+15+19+23......)

Common difference = 4

now by putting Sn formula

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

Putting values we get

12561