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Chapter 12: Q. 55 (page 817)

Find x so that x + 3, 2x + 1, and 5x + 2 are consecutive terms of an arithmetic sequence.

Short Answer

Expert verified

The value of x is $- \frac{3}{2}$

Step by step solution

01

Given Information

x + 3, 2x + 1, and 5x + 2 are consecutive terms of an arithmetic sequence

02

common difference

$a_{1} = x + 3 a_{2} = 2 x + 1 a_{3} = 5 x + 2 a_{2} - a_{1} = 2 x + 1 - (x + 3) = x - 2 a_{3} - a_{2} = 5 x + 2 - (2 x + 1) = 3 x + 1$

03

common difference is a constant

common difference is constant in arithmetic sequence

$a_{2} - a_{1} = a_{3} - a_{2} x - 2 = 3 x + 1 x - 3 x - 2 = 1 - 2 x - 2 = 1 - 2 x = 1 + 2 - 2 x = 3 x = - \frac{3}{2} t h e v a l u e o f x = - \frac{3}{2}$

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Most popular questions from this chapter

Problems 17–28, write down the first five terms of each sequence.

$\{c_{n}\} = \{{(- 1)}^{n + 1} n^{2}\}$

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.

$\frac{2}{3}, \frac{4}{9}, \frac{8}{27}, \frac{16}{81}, . . .$

In Problems 71-82, find the sum of each sequence.

${\sum (3}_{k = 1}^{26} k - 7)$

In Problems 71-82, find the sum of each sequence.

${\sum (-}_{k = 1}^{24} k)$

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.

$a_{1} = - 2; a_{n} = n + a_{n - 1}$

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