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Chapter 14: Problem 7

Write the first five terms of each arithmetic sequence. $$ a_{1}=5, d=4 $$

Short Answer

Expert verified
The first five terms are 5, 9, 13, 17, 21.

Step by step solution

01

Understand the formula

In an arithmetic sequence, each term is found by adding a constant difference (d) to the previous term. The formula for the nth term is given by: \[ a_n = a_1 + (n-1)d \] where \( a_1 \) is the first term and \( d \) is the common difference.
02

Identify the given values

The first term \( a_1 \) is given as 5, and the common difference \( d \) is given as 4.
03

Calculate the first term

The first term \( a_1 \) is given directly, so \( a_1 = 5 \).
04

Calculate the second term

Using the formula, substitute \( n = 2 \): \[ a_2 = a_1 + (2-1)d = 5 + 1 \times 4 = 9 \]
05

Calculate the third term

Using the formula, substitute \( n = 3 \): \[ a_3 = a_1 + (3-1)d = 5 + 2 \times 4 = 13 \]
06

Calculate the fourth term

Using the formula, substitute \( n = 4 \): \[ a_4 = a_1 + (4-1)d = 5 + 3 \times 4 = 17 \]
07

Calculate the fifth term

Using the formula, substitute \( n = 5 \): \[ a_5 = a_1 + (5-1)d = 5 + 4 \times 4 = 21 \]
08

List the first five terms

The first five terms of the arithmetic sequence are: \( 5, 9, 13, 17, 21 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

nth term formula
Understanding the formula to find the nth term of an arithmetic sequence is crucial. The formula is given by: \[ a_n = a_1 + (n-1)d \]. This means each term in the sequence (\( a_n \)) is equal to the first term (\( a_1 \)) plus the product of the common difference (\

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