Question

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

Answer 1

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 = $a_{1}=13$
Fourth term of sequence = $a_{4}=88$

$a_{4}= a_{1}+3d$

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

$88=13+3d \\ \\ 3d = 88 - 13 \\ \\ 3d=75 \\ \\ d=25$

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

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

And,
y = $a_{1}+2d=13+2(25)=63$

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

13, 38, 63, 88