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Chapter 5: Problem 5

Write the first six terms of the arithmetic sequence with the first term, \(a_{1}\), and common difference, \(d\). \(a_{1}=-7, d=4\)

Short Answer

Expert verified
The first six terms of the arithmetic sequence are -7, -3, 1, 5, 9, 13.

Step by step solution

01

Identify the first term and common difference

From the problem given, the first term, denoted as \(a_{1}\), is -7 and the common difference, denoted as \(d\), is 4.
02

Apply the arithmetic sequence rule

The formula for the \(n\)th term of an arithmetic sequence is: \(a_{n} = a_{1} + (n - 1)*d\). Here, we substitute \(n\) with the positions 2 to 6 to get the next five terms.
03

Calculate the next five terms

By substituting \(n=2\) to \(6\) into the formula, we get the second term as \(a_{2} = a_{1} + (2 - 1)*d = -7 + 4 = -3\), the third term as \(a_{3} = a_{1} + (3 - 1)*d = -7 + 4*2 = 1\), the fourth term as \(a_{4} = a_{1} + (4 - 1)*d = -7 + 4*3 = 5\), the fifth term as \(a_{5} = a_{1} + (5 - 1)*d = -7 + 4*4 = 9\), and the sixth term as \(a_{6} = a_{1} + (6 - 1)*d = -7 + 4*5 = 13\).

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