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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

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.

1 + 5 + 9 + + 401

To determine

The partial sum of the arithmetic sequence 1+5+9++401.

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,

1+5+9++401

Calculation:

Calculate the nth term of the sequence.

Since from the partial sum of the arithmetic sequence, the first term will be 1 and the common difference between two consecutive terms is 4.

Substitute 401 for an, 1 for a1 and 4 for d in the equation (1)

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