Question

What is the sum of the first 14 terms of the series 9, 2, – 5, – 12, – 19, – …?

a. –25
b. –98
c. –511
d. –518

Answer 1

To find the sum of the first 14 terms of the given arithmetic series, use the formula for the sum of an arithmetic series, substituting the given values and simplifying the expression.

Step-by-step explanation:

The given series is an arithmetic sequence, where the first term is 9 and the common difference is -7. To find the sum of the first 14 terms of the series, we can use the formula for the sum of an arithmetic series:

S = (n/2)(2a + (n-1)d)

where S is the sum, n is the number of terms, a is the first term, and d is the common difference.

Substituting the given values into the formula:

S = (14/2)(2(9) + (14-1)(-7))

Simplifying:

S = 7(18 - 13(-7))

S = 7(18 + 91)

S = 7(109)

S = 763

Therefore, the sum of the first 14 terms of the series is 763.