Chapter 11: Q8. (page 581)

Find the $a_{13}$ for the arithmetic sequence -17, -12, -7, ….

Short Answer

Expert verified

The $a_{13}$ for the arithmetic sequence is43.

Step by step solution

Step 1. Given Information.

Given arithmetic sequence is -17, -12, -7, ….

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 $a_{1} = - 17$

The difference between the first two terms is $- 12 - (- 17) = - 12 + 17 = 5$

The difference between the next two terms is $- 7 - (- 12) = - 7 + 12 = 5$

Hence, the common difference is $d = 5$

And the required term is $n = 13$

Plugging the values in the formula:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ a_{13} = - 17 + (13 - 1) (5) \\ a_{13} = - 17 + (12) (5) \\ a_{13} = - 17 + 60 \\ a_{13} = 43 \end{array}$

Step 3. Conclusion.

Hence, the $a_{13}$ for the arithmetic sequence is 43.

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Find the $a_{13}$ for the arithmetic sequence -17, -12, -7, ….

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Find the a13 for the arithmetic sequence -17, -12, -7, ….

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

Geometry

Discrete Mathematics

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the $a_{13}$ for the arithmetic sequence -17, -12, -7, ….