Question

arithmetic series:

1. a) determine the sum of the first 16 terms of the following arithmetic series?

254 + 271 + 288 + .........

Explanation:

Step1: Identify a, d, n

In an arithmetic series, \( a_1 = 254 \) (first term), common difference \( d = 271 - 254 = 17 \), number of terms \( n = 16 \).

Step2: Use sum formula

The formula for the sum of the first \( n \) terms of an arithmetic series is \( S_n=\frac{n}{2}[2a_1+(n - 1)d] \).
Substitute \( n = 16 \), \( a_1 = 254 \), \( d = 17 \):

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Answer:

The sum of the first 16 terms is 6104.