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

The sum of the first 28 terms in the sequence is 5600

Sum of sequence

The sum of sequences are known as series. Given the following

a₁ = 92

a₁ = ai-1 - 8

For the second term

a2 = a1 - 8

a2 = 92 - 8

a2 = 84

Determine the sum of first 28th terms

S28 = 28/2[2(92)+(28-1)(8)]

S28 = 14(184+27(8))
S28 = 14(400)
S28 = 5600

Hence the sum of the first 28 terms in the sequence is 5600

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Answer 2

Answer:

  -448

Step-by-step 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

__

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.