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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

27-32 ■ Arithmetic Sequence? Find the first five terms of the sequence, and determine whether it is arithmetic. If it is arithmetic, find the common difference, and express the nth term of the sequence in the standard form a n = a + ( n 1 ) d .

a n = 1 + n 2

To determine

The first five terms of the sequence an=1+n2, if it is arithmetic the values of the common difference and the nth term of the sequence in the standard form.

Explanation

Approach:

An arithmetic sequence is a sequence of the form,

a,a+d,a+2d,a+3d,a+4d,

Here, a is the first term and d is the difference between two consecutive terms.

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.

Calculation:

Calculate the first term of the sequence.

Substitute 1 for n in the nth sequence to calculate the first term.

a1=1+12=32

Calculate the second term of the sequence.

Substitute 2 for n in the nth sequence to calculate the second term.

a2=1+22=2

Calculate the third term of the sequence.

Substitute 3 for n in the nth sequence to calculate the third term.

a3=1+32=52

Calculate the fourth term of the sequence.

Substitute 4 for n in the nth sequence to calculate the fourth term.

a4=1+42=3

Calculate the fifth term of the sequence.

Substitute 5 for n in the nth sequence to calculate the fifth term.

a5=1+52=72

Therefore, the first five sequence is 32,2,52,3,72.

Since in the arithmetic sequence, any two consecutive terms of the sequence differ by d

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