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Chapter 11: Q13. (page 581)

Find the three arithmetic means between 44 and 92.

Short Answer

Expert verified

The three arithmetic means between 44 and 92 are56, 68, 80.

Step by step solution

01

Step 1. Given Information.

Given there are three arithmetic means between 44 and 92.

02

Step 2. Calculation.

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

Since there are three arithmetic means between 44 and 92,

The first term is a1=44

And the fifth term is a5=92

Plugging the values in the formula:

an=a1+(n鈭�1)da5=a1+(5鈭�1)d92=44+4d4d=92鈭�444d=48d=12

Hence the common difference is 12.

Since the first term in the arithmetic sequence is 44:

The next term in the arithmetic sequence is 44+12=56

The next term in the arithmetic sequence is 56+12=68

The next term in the arithmetic sequence is 68+12=80

And the fifth term in the arithmetic sequence is 92.

03

Step 3. Conclusion.

Hence, the three arithmetic means between 44 and 92 are 56, 68, 90.

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