Question

How do you find the sum of the arithmetic series `Sigma(2-3n)` from n=1 to 5?

Answer 1

`Sum = -35`

Explanation:

Formula for sum of n terms in A.P
`Sum = n(a_1 + a_n) = (n/2)(2a_1 + (n-1) * d)`

First term `a_1 = 2-(3*1) = -1`
Second term `a_2 = 2 -(3*2) = -4`
`d = a_2 - a_1 = -4 - (-1 ) = -3`
`n = 5`

`Sum = (5/2)[(2*(-1)) + (5-1) *(-3)]`

`Sum = (5/2)[-2 + 4*(-3)] = (5/2)[-2-12] = -35`