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Chapter 5: Problem 4

Write the first six terms of the arithmetic sequence with the first term, \(a_{1}\), and common difference, \(d\). \(a_{1}=300, d=50\)

Short Answer

Expert verified
The first six terms of the arithmetic sequence are 300, 350, 400, 450, 500, 550.

Step by step solution

01

Determine the First Term

The first term, or \(a_{1}\), is given as 300. Therefore, we already know the first term of the sequence is 300.
02

Find the Second Term

Use the formula \(a_{n} = a_{1} + (n - 1) * d\) to find the second term, \(a_{2}\). Substitute 1 for n, 300 for \(a_{1}\), and 50 for d into the formula, resulting in \(a_{2} = 300 + (1 - 1) * 50\). Simplifying this equation yields \(a_{2} = 350\).
03

Find the Third Term

Once again, use the formula \(a_{n} = a_{1} + (n - 1) * d\) to find the third term, \(a_{3}\). Substitute 2 for n, 300 for \(a_{1}\), and 50 for d into the formula, resulting in \(a_{3} = 300 + (2 - 1) * 50\). Simplifying this equation yields \(a_{3} = 400\).
04

Find the Fourth Term

Using the formula \(a_{n} = a_{1} + (n - 1) * d\) for the fourth term, \(a_{4}\), we substitute 3 for n, 300 for \(a_{1}\), and 50 for d. This results in \(a_{4} = 300 + (3 - 1) * 50\). Simplifying this equation yields \(a_{4} = 450\).
05

Find the Fifth Term

We find the fifth term, \(a_{5}\), the same way by substituting 4 for n, 300 for \(a_{1}\), and 50 for d in the formula \(a_{n} = a_{1} + (n - 1) * d\). This gives \(a_{5} = 300 + (4 - 1) * 50\), which simplifies to \(a_{5} = 500\).
06

Find the Sixth Term

Finally, we find the sixth term, \(a_{6}\), by substituting 5 for n, 300 for \(a_{1}\), and 50 for d in the formula \(a_{n} = a_{1} + (n - 1) * d\). This gives \(a_{6} = 300 + (5 - 1) * 50\), which simplifies to \(a_{6} = 550\).

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(6,3, \frac{3}{2}, \frac{3}{4}, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{200}\), when \(a_{1}=60, r=1\).

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(-7,-2,3,8, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-6, r=-5\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-1000, r=0.1\)
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