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