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Chapter 5: Problem 7

Write the first six terms of the arithmetic sequence with the first term, \(a_{1}\), and common difference, \(d\). \(a_{1}=-400, d=300\)

Short Answer

Expert verified
The first six terms of the arithmetic sequence are: -400, -100, 200, 500, 800, 1100

Step by step solution

01

Understanding the Sequence

An arithmetic sequence is defined by its first term \(a_{1}\) and the common difference \(d\). the nth term \(a_{n}\) of an arithmetic sequence can be found by the formula: \(a_{n} = a_{1} + (n-1) * d\). In this case, \(a_{1} = -400\) and \(d = 300\).
02

Find the second term

Plug the values into the formula to get the second term \(a_{2}\). This gives \(a_{2} = -400 + (2-1) * 300 = -100.\)
03

Find the third term

Substitute the values into the formula to get the third term \(a_{3}\). This gives \(a_{3} = -400 + (3-1) * 300 = 200.\)
04

Find the fourth term

Substitute the values into the formula to get the fourth term \(a_{4}\). This gives \(a_{4} = -400 + (4-1) * 300 = 500.\)
05

Find the fifth term

Substitute the values into the formula to get the fifth term \(a_{5}\). This gives \(a_{5} = -400 + (5-1) * 300 = 800.\)
06

Find the sixth term

Substitute the values into the formula to get the sixth term \(a_{6}\). This gives \(a_{6} = -400 + (6-1) * 300 = 1100.\)

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