Question

Find the sum of -50 + (-44) + (-38) + ... + 2038 + 2044.

Answer 1

3950

Step-by-step explanation:

-50 + (-44) + (-38) + 2038 + 2044

-94 + (-38) + 2038 + 2044

-132 + 2038 + 2044

1906 + 2044

3950
Hope this helps :)

Answer 2

348950

Step-by-step explanation:

• first lets confirm, which series this is from,

( first term + third term )/2 = second term

• (-50 + (-38) )/2 = -44

• -44 = -44

Thus it is arithmetic series.

`\sf S_n = (n)/(2) (2a+(n-1)d)`

Solving step-wise:

• a₁ = -50

• aₙ = 2044

• n = ? = 350

• d = + 6

=================

• aₙ = a₁ + d(n-1)

• 2044 = -50 + 6(n-1)

• 6(n) - 6 = 2094

• 6(n) = 2100

• n = 350

Here,

`\sf S_n = (n)/(2) (2a+(n-1)d)`

`\sf S_n = (350)/(2) (2(-50)+(350-1)(6))`

`\sf S_n =348950`