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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

11-14 Arithmetic or Geometric The n th term of sequence is given. (a) Find the first five terms of the sequence. (b) Graph the terms you found in part (a). (c) Find the fifth partial sum of the sequence. (d) Determine whether the sequence is arithmetic or geometric. Find the common difference or the common ratio.

a n = 3 n 2 n + 1

To determine

(a)

The first five terms of the sequence whose nth term is an=3n2n+1

Explanation

Approach:

A sequence is a function whose domain is the set of natural numbers. The terms of a sequence are the function values,

a1,a2,...,an

Where, a1 is the first term, a2 is the second term and an is the nth term of the sequence.

Calculations:

Consider the nth term,

an=3n2n+1 (1)

Substitute 1 for n in equation (1), to calculate first term,

a1=3121+1=322=34

Substitute 2 for n in equation (1), to calculate second term,

a2=3222+1=3223=98

Substitute 3 for n in equation (1), to calculate third term,

To determine

(b)

To plot:

The graph for the terms obtained in part (a).

To determine

(c)

The fifth partial sum of the sequence 34,98,2716,8132,24364

To determine

(d)

The sequence 34,98,2716,8132,24364 is arithmetic or geometric and the common difference or common ration of the sequence.

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