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Chapter 12: Q. 23 (page 816)

Find the indicated term in each arithmetic sequence.
$100$ th term of $2, 4, 6, . . . . .$

Short Answer

Expert verified

The solution is $200$ .

Step by step solution

01

Step 1. Given information

Arithmetic sequence: $2, 4, 6, . . . .$

02

Step 2. Calculation

The first term of the arithmetic sequence is $a_{1} = 2$ , and the common difference is $d = 2$ .

Now, the $100$ th term is -

$a_{n} = a_{1} + (n - 1) d$

role="math" localid="1648710235562" $a_{100} = 2 + (100 - 1) 2$

$= 2 + 198$

$= 200$

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Most popular questions from this chapter

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

role="math" localid="1646738144824" $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, . . .$

In Problems 51–60, write out each sum.

$\sum_{k = 3}^{n} {(- 1)}^{k + 1} 2^{k}$

True or False. The notation $a_{5}$ represents the fifth term of a sequence.

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

$a_{1} = \sqrt{2}; a_{n} = \sqrt{\frac{a_{n - 1}}{2}}$

In Problems 11–16, evaluate each factorial expression.

$\frac{9!}{6!}$

See all solutions

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