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Chapter 5: Problem 13

Write the first six terms of the arithmetic sequence with the first term, \(a_{1}\), and common difference, \(d\). \(a_{1}=\frac{5}{2}, d=\frac{1}{2}\)

Short Answer

Expert verified
The first six terms of the arithmetic sequence are: \(\frac{5}{2}, \frac{6}{2}, \frac{7}{2}, \frac{9}{2}, \frac{11}{2}, \frac{13}{2}\)

Step by step solution

01

Identify the first term and the common difference

The first term, \(a_{1} = \frac{5}{2}\) and the common difference \(d = \frac{1}{2}\) are given in the exercise.
02

Use the formula of nth term of arithmetic sequence

The nth term of an arithmetic sequence is given by: \(a_{n} = a_{1} + (n-1)d\). Hence, plug the values of \(a_{1}\) and \(d\) into this formula to find the next terms of the sequence.
03

Find the second term

The second term can be calculated as follows: \(a_{2} = a_{1} + (2-1)d = \frac{5}{2} + \frac{1}{2} = \frac{6}{2}\).
04

Find the third term

Calculate the third term: \(a_{3} = a_{1} + (3-1)d = \frac{5}{2} + 2 \cdot \frac{1}{2} = \frac{7}{2}\).
05

Find the rest of the terms

Continue in this same way to get term four, five, and six: \(a_{4} = \frac{9}{2}, a_{5} = \frac{11}{2}, a_{6} = \frac{13}{2}\).

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Most popular questions from this chapter

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(18,6,2, \frac{2}{3}, \ldots\)

Use the appropriate formula shown above to find \(2+4+6+8+\cdots+200\), the sum of the first 100 positive even integers.

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-2, r=-3\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2000, r=-1\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2, r=3\)
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