Question

An arithmetic sequence is defined as follows:

a₁ = 92
a₁ = a₁-1-8
Find the sum of the first 28 terms in the sequence.

Answer 1

-448

Explanation:

The sum of 28 terms of the arithmetic sequence with first term 92 and common difference -8 can be found using the formula for the sum of an arithmetic series.

Sn = (2a1 +d(n -1))(n/2) . . . . sum of n terms with first term a1, difference d

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series sum

Using the above formula with a1=92, d=-8, and n=28, the sum is ...

S28 = (2·92 -8(28 -1))/(28/2) = (184 -216)(14) = -448

The sum of the first 28 terms of the sequence is -448.