Q54.

Find the arithmetic means in each sequence.

-8, ? , ? , ?, ? , 7

Verified

Answer

The arithmetic means in the sequence are -5, -2, 1, 4.

1Step 1. Given Information.

Given there are four arithmetic means between -8 and 7.

2Step 2. Calculation .

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

Since there are four arithmetic means between -8 and 7,

The first term is $a_{1} = - 8$

And the sixth term is $a_{6} = 7$

Plugging the values in the formula:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ a_{6} = a_{1} + (6 - 1) d \\ 7 = - 8 + 5 d \\ 5 d = 7 + 8 \\ 5 d = 15 \\ d = 3 \end{array}$

Hence the common difference is 3.

Since the first term in the arithmetic sequence is -8:

The next term in the arithmetic sequence is $- 8 + 3 = - 5$

The next term in the arithmetic sequence is $- 5 + 3 = - 2$

The next term in the arithmetic sequence is $- 2 + 3 = 1$

The next term in the arithmetic sequence is $1 + 3 = 4$

And the sixth term in the arithmetic sequence is 7.

3Step 3. Conclusion .

Hence, the arithmetic means in the sequence are -5, -2, 1, 4.