Chapter 11: Q52. (page 582)

Find the arithmetic means in each sequence.
55, ? , ? , ? , 115

Short Answer

Expert verified

The arithmetic means in the sequence are70, 85, 100.

Step by step solution

Step 1. Given Information.

Given there are three arithmetic means between 55 and 115.

Step 2. Calculation.

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

Since there are three arithmetic means between 55 and 115,

The first term is $a_{1} = 55$

And the fifth term is $a_{5} = 115$

Plugging the values in the formula:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ a_{5} = a_{1} + (5 - 1) d \\ 115 = 55 + 4 d \\ 4 d = 115 - 55 \\ 4 d = 60 \\ d = 15 \end{array}$

Hence the common difference is 15.

Since the first term in the arithmetic sequence is 55:

The next term in the arithmetic sequence is $55 + 15 = 70$

The next term in the arithmetic sequence is $70 + 15 = 85$

The next term in the arithmetic sequence is $85 + 15 = 100$

And the fifth term in the arithmetic sequence is 115.

Step 3. Conclusion.

Hence, the arithmetic means in the sequence are 70, 85, 100.

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Find the arithmetic means in each sequence.
55, ? , ? , ? , 115

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.55, ? , ? , ? , 115

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

Decision Maths

Geometry

Pure Maths

Probability and Statistics

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Find the arithmetic means in each sequence.
55, ? , ? , ? , 115