Q53.

Find the arithmetic means in each sequence.

10, ? , ? , -8

Verified

Answer

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

1Step 1. Given Information.

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

2Step 2. Calculation .

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

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

The first term is $a_{1} = 10 a$

And the fourth term is $a_{4} = - 8$

Plugging the values in the formula:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ a_{4} = a_{1} + (4 - 1) d \\ - 8 = 10 + 3 d \\ 3 d = - 8 - 10 \\ 3 d = - 18 \\ d = - 6 \end{array}$

Hence the common difference is -6.

Since the first term in the arithmetic sequence is 10:

The next term in the arithmetic sequence is $10 - 6 = 4$

The next term in the arithmetic sequence is $4 - 6 = - 2$

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

3Step 3. Conclusion .

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