SOLUTION: Insert the indicated number of arithmetic means between the two given numbers Three; a+2 and 5a-10 So it looks like this a+2 _ _

SOLUTION: Insert the indicated number of arithmetic means between the two given numbers Three; a+2 and 5a-10 So it looks like this a+2 _ _ _ 5a-10 Find the three terms between

Question 1039313: Insert the indicated number of arithmetic means between the two given numbers
Three; a+2 and 5a-10
So it looks like this
a+2 _ _ _ 5a-10
Find the three terms between them
Thank you please help me
Please with solution so i can study it myself
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
ONE WAY TO GET TO THE ANSWER (Probably the expected way):
When you fill in the blanks, the five numbers (or expressions) form an arithmetic sequence.
is the firs term of the sequence.
is the fifth element of the sequence.
In an arithmetic sequence each term is the one before plus a common difference, .
In formulas, that is written as
, or .
As a consequence, any term is related to the first term, and the common difference by the formula

So, for , <--->
Since we know and , we can substitute those expressions and solve for :
---> ---> ---> ---> .
Now, we can find the missing terms:
The second term is
.
The third term is
.
The fourth term is
.

ANOTHER WAY (This works only for sequences with an odd number of terms):
When three numbers are in an arithmetic sequence,
the middle term is the average of the first and last terms.
The same thing happens when in the sequence there are
5 terms, 7 terms, 9 terms, 11 terms, and so on.
So, the middle (third) term is
.
The second number, the one between and is
.
The fourth number, the one between and is
.
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