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Chapter 14: Problem 3

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

Short Answer

Expert verified
The first four terms of the sequence described by the general term \(a_{n}=3^{n}\) are 3, 9, 27, 81.

Step by step solution

01

Identify the general formula

The general formula for the sequence is \(a_{n} = 3^{n}\), where 'n' represents the term number and \(a_{n}\) represents the particular term in the sequence.
02

Calculate 1st Term

Substitute 'n' with 1 in the formula \(a_{n} = 3^{n}\) to get the first term. This gives \(a_{1} = 3^{1} = 3\).
03

Calculate 2nd Term

Substitute 'n' with 2 in the formula \(a_{n} = 3^{n}\) to get the second term. This gives \(a_{2} = 3^{2} = 9\).
04

Calculate 3rd Term

Substitute 'n' with 3 in the formula \(a_{n} = 3^{n}\) to get the third term. This results in \(a_{3} = 3^{3} = 27\).
05

Calculate 4th Term

Substitute 'n' with 4 in the formula \(a_{n} = 3^{n}\) to get the fourth term. This results in \(a_{4} = 3^{4} = 81\).

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