Question

Arithmetic Series:
Find the sum of -50 + -44 + -38 +... + 2038 + 2044

Answer 1

The sum of the given series is 348950.

Explanation:

Given,

The series is : -50+(-44)+(-38)+...+2038+2044

To find the sum of the series.

Formula

• The sum of the nth order arithmetic series where a is the initial term and d is the common difference
  `S_(n)` =
  `(n)/(2)`[2a+(n-1)d]

• Last term
  `a_(n)` = a+(n-1)d

Now,

Initial term (a) = -50

Common difference (d) = -44 - (-50) = -44+50 = 6

According to the problem,

-50+(n-1)6 = 2044

or, (n-1)6 = 2094

or, n-1 = 349

or, n = 350

Now,

The sum
`S_(n)` =
`(350)/(2)`[2×(-50)+(350-1)×6]

= 348950

Hence,

The sum is 348950.