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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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Most popular questions from this chapter

Refer to the first three arrays of numbers below.

Is 397 a number in this pattern? Explain.

Find the next four terms of each arithmetic sequence.

12, 16, 20, 鈥�

To prove that objects of different weights fall at the same rate, Galileo dropped two objects with different weights from the Leaning Tower of Pisa in Italy. The objects hit the ground at the same time. When an object is dropped from a tall building, it falls about 16 feet in the first second, 48 feet in the second second, and 80 feet in the third second, regardless of its weight.How many feet would an object fall in the tenth second?

Find the indicated term of each arithmetic sequence.

a1=鈭�4,d=鈭�9,n=20

Find the arithmetic means in each sequence.

55, ? , ? , ? , 115
See all solutions

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