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Chapter 8: Problem 10

Write the first four terms of each sequence whose general term is given. $$a_{n}=\frac{3 n}{n+5}$$

Short Answer

Expert verified
The first four terms of the sequence are \(a_{1}=\frac{1}{2}\), \(a_{2}=\frac{6}{7}\), \(a_{3}=\frac{9}{8}\), and \(a_{4}=\frac{4}{3}\).

Step by step solution

01

Understand the general term of the sequence

The given general term is \(a_{n}=\frac{3 n}{n+5}\). \(a_{n}\) represents the nth term in the sequence, hence, to generate the sequence it's required to substitute integer values of n starting from 1.
02

Calculate the first term

Substitute n = 1 into the general term \(a_{n}\) to find the first term. i.e, \(a_{1}=\frac{3 \times 1}{1+5}=\frac{1}{2}\)
03

Calculate the second term

Substitute n = 2 into the general term \(a_{n}\) to find the second term. i.e, \(a_{2}=\frac{3 \times 2}{2+5}=\frac{6}{7}\)
04

Calculate the third term

Substitute n = 3 into the general term \(a_{n}\) to find the third term. i.e, \(a_{3}=\frac{3 \times 3}{3+5}=\frac{9}{8}\)
05

Calculate the fourth term

Substitute n = 4 into the general term \(a_{n}\) to find the fourth term. i.e, \(a_{4}=\frac{3 \times 4}{4+5}=\frac{4}{3}\)

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