Insert the given variety of arithmetic way between the numbers.

You are watching: Form a sequence that has two arithmetic means between -13 and 89.

EXAMPLE

Insert two arithmetic means between 6 and 27.

Strategy because two arithmetic means are to it is in inserted between 6 and 27, us will consider a sequence of four terms, v a very first term of 6 and a 4th term of 27. We will then usage an = a1 + (n − 1)d to discover the usual difference d.

Why once we know the an initial term and also the common difference, us can include the common difference to find the two unknown terms.

Solution

The first term is a1 = 6 and the 4th term is a4 = 27. We must find the usual difference so the the terms

form one arithmetic sequence. To find the common difference d, us substitute 6 for a1; 4 because that n, and 27 for a4in the formula for the fourth term:

To find the two arithmetic means between 6 and also 27, we include the usual difference 7, as shown:

Two arithmetic method between 6 and also 27 room 13 and also 20.

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Three arithmetic way between 20 and 30

We need to insert three arithmetic method between 20 and also 30.

Since we have to insert four arithmetic means between 20 and 30, we think about a succession of five terms with the first term

and the 5th term