Chapter 11: Q53. (page 582)

Find the arithmetic means in each sequence.
10, ? , ? , -8

Short Answer

Expert verified

The arithmetic means in the sequence are4, -2.

Step by step solution

Step 1. Given Information.

Given there are two arithmetic means between 10 and -8.

Step 2. Calculation.

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

Since there are two arithmetic means between 10 and -8,

The first term is $a_{1} = 10 a$

And the fourth term is $a_{4} = - 8$

Plugging the values in the formula:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ a_{4} = a_{1} + (4 - 1) d \\ - 8 = 10 + 3 d \\ 3 d = - 8 - 10 \\ 3 d = - 18 \\ d = - 6 \end{array}$

Hence the common difference is -6.

Since the first term in the arithmetic sequence is 10:

The next term in the arithmetic sequence is $10 - 6 = 4$

The next term in the arithmetic sequence is $4 - 6 = - 2$

And the fourth term in the arithmetic sequence is -8.

Step 3. Conclusion.

Hence, the arithmetic means in the sequence are 4, -2.

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Find the arithmetic means in each sequence.
10, ? , ? , -8

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Find the arithmetic means in each sequence.10, ? , ? , -8

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

Calculus

Geometry

Applied Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find the arithmetic means in each sequence.
10, ? , ? , -8