   Chapter 13.2, Problem 58E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# 57-64 Partial Sums of an Arithmetic Sequence A partial sum of an arithmetic sequence is given. Find the sum. − 3 + ( − 3 2 ) + 0 + 3 2 + 3 + ⋯ + 30

To determine

The partial sum of the arithmetic sequence.

Explanation

Approach:

The nth term of an arithmetic sequence in standard form is given by,

an=a1+(n1)d ……(1)

Here, an is the nth term, a1 is the first term, n is the number of terms and d is the difference between two consecutive terms.

The partial sum of an arithmetic sequence is given as,

Sn=n(a+an2) ……(2)

Here, Sn is the partial sum of n terms, n is the number of terms and a is the first term of the sequence.

Given:

The partial sum of an arithmetic sequence is given as,

3+(32)+0+32+3++30

Calculation:

Calculate the nth term of the sequence.

Since from the partial sum of the arithmetic sequence, the first term will be 3 and the common difference between two consecutive terms is 32.

Substitute 30 for an, 3 for a1 and 32 for d in the equation (1)

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