Form a sequence that has two arithmetic means between 13 and 88.

Let x and y be the two arithmetic means between 13 and 88. So the complete sequence will be:

13, x, y, 88

First term of sequence = [tex] a_{1}=13 [/tex]
Fourth term of sequence = [tex] a_{4}=88 [/tex]

[tex] a_{4}= a_{1}+3d \\ \\ [/tex]

Using the value of [tex] x_{4} [/tex] and [tex] x_{1} [/tex], we can calculate the value of d which is the common difference of the series.

[tex]88=13+3d \\ \\ 3d = 88 - 13 \\ \\ 3d=75 \\ \\ d=25[/tex]

Therefore, the common difference of the sequence will be 25.

x is the second term of the sequence.
So, x = [tex] a_{1}+d=13+25=38 [/tex]

And,
y = [tex] a_{1}+2d=13+2(25)=63 [/tex]

Therefore, the first four terms of the sequence will be:

13, 38, 63, 88