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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

01

Step 1. Given Information.

Given there are three arithmetic means between 55 and 115.

02

Step 2. Calculation.

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

Since there are three arithmetic means between 55 and 115,

The first term is a1=55

And the fifth term is a5=115

Plugging the values in the formula:

an=a1+(n鈭�1)da5=a1+(5鈭�1)d115=55+4d4d=115鈭�554d=60d=15

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.

03

Step 3. Conclusion.

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

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