Question

98. What is the sum of the first 27 terms in the arithmetic series 25 +19+13 + ...?​

Answer 1

sum of the first 27 terms = -1431

Explanation:

arithmetic series sum of the first n terms formula:

`s_(n) = (n)/(2) (2a + (n - 1)d)`

n = 27 terms

first term, a = 25

common difference, d = 19 - 25 = -6

substitute the values into the formula

`s_(27) = (27)/(2) (2(25) + (27 - 1)( - 6))`

`s_(27) = 13.5(50 + 26( - 6))`

`s_(27) = 13.5(50 - 156)`

`s_(27) = 13.5( - 106)`

`s_(27) = - 1431`