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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

01

Step 1. Given Information.

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

02

Step 2. Calculation.

The nth term of an arithmetic sequence is given by an=a1+(n鈭�1)d.

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

The first term is a1=10a

And the fourth term is a4=鈭�8

Plugging the values in the formula:

an=a1+(n鈭�1)da4=a1+(4鈭�1)d鈭�8=10+3d3d=鈭�8鈭�103d=鈭�18d=鈭�6

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鈭�6=4

The next term in the arithmetic sequence is 4鈭�6=鈭�2

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

03

Step 3. Conclusion.

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

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