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Chapter 22: Problem 675

If an arithmetic progression is generated by the linear function \(\mathrm{F}(\mathrm{x})=-3 \mathrm{x}+14\), what is the first term? What is the 15 th term? What is the common difference?

Short Answer

Expert verified
The first term of the arithmetic progression is \(11\), the 15th term is \(-31\), and the common difference is \(-3\).

Step by step solution

01

Find the first term

To find the first term of the arithmetic progression, we substitute \(x = 1\) into the function: \(F(1) = -3(1) + 14 = -3 + 14 = 11\) The first term of the arithmetic progression is 11.
02

Find the 15th term

To find the 15th term of the arithmetic progression, we substitute \(x = 15\) into the function: \(F(15) = -3(15) + 14 = -45 + 14 = -31\) The 15th term of the arithmetic progression is -31.
03

Find the common difference

The common difference in an arithmetic progression generated by a linear function is simply the coefficient of the x-term. In this case, the coefficient of \(x\) is \(-3\). The common difference of the arithmetic progression is -3.

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Most popular questions from this chapter

Find the seventh term of a geometric series whose third term is \(1 / 8\) and common ratio is \(2 .\) Find the first seven terms.

Sum the sequence \(2 / 3,-1,3 / 2, \ldots \ldots\) to 7 term.

If the first term of an arithmetic progression is 7, and the common difference is \(-2\), find the fifteenth term and the sum of the first fifteen terms.

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