Chapter 11: Q45. (page 582)

Complete the statement for each arithmetic sequence.
-14 is the _? term of $2 \frac{1}{5}, 2, 1 \frac{4}{5}, ...$ .

Short Answer

Expert verified

-14 is the82nd termof the arithmetic sequence $2 \frac{1}{5}, 2, 1 \frac{4}{5}, ...$ .

Step by step solution

Step 1. Given Information.

Given arithmetic sequence is $2 \frac{1}{5}, 2, 1 \frac{4}{5}, ...$

Step 2. Calculation.

The n^th term of an arithmetic sequence is given by $a_{n} = a_{1} + (n - 1) d$ .

Here the first term is $a_{1} = 2 \frac{1}{5}$

The difference between the first two terms is $2 - 2 \frac{1}{5} = - \frac{1}{5}$

The difference between the second two terms is $1 \frac{4}{5} - 2 = - \frac{1}{5}$

The common difference is $d = - \frac{1}{5}$

The given nth term is $a_{n} = - 14$

Plugging the values in the formula:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ - 14 = 2 \frac{1}{5} + (n - 1) (- \frac{1}{5}) \\ - 14 - 2 \frac{1}{5} = (n - 1) (- \frac{1}{5}) \\ (n - 1) (- \frac{1}{5}) = - \frac{81}{5} \\ n - 1 = 81 \\ n = 81 + 1 \\ n = 82 \end{array}$

Step 3. Conclusion.

Hence, -14 is the 82nd term of the arithmetic sequence $2 \frac{1}{5}, 2, 1 \frac{4}{5}, ...$ .

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Complete the statement for each arithmetic sequence.
-14 is the _? term of $2 \frac{1}{5}, 2, 1 \frac{4}{5}, ...$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Complete the statement for each arithmetic sequence.-14 is the ___?__ term of 215,2,145,....

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Complete the statement for each arithmetic sequence.
-14 is the _? term of $2 \frac{1}{5}, 2, 1 \frac{4}{5}, ...$ .