SOLUTION: Given that four integers are consecutive terms of an arithmetic sequence with sum 24 and product 945, what is the biggest of these four integers?

Question 1055828: Given that four integers are consecutive terms of an arithmetic sequence with sum 24 and product 945, what is the biggest of these four integers?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Since it is about 4 integers, consider divisibility.
is the factorization for 945.
You notice that 3, 5, and 7 are factors of 945,
and the form an arithmetic sequence!
If those were 3 of the 4 factors whose product is 954,
The fourth factor would be
.
So, ,
and those 4 factors form an arithmetic sequence.
Of course, , , , and are another answer.

USING EQUATIONS:
= common difference of the arithmetic sequence.
= average (mean) and median of thev4 numbers.
Then, the numbers are
, , , and .
The product is

So,
EITHER, ---> ,
which gives you the two arithmetic sequences found before,
OR , which gives you
two arithmetic sequences of four (irrational) numbers,
asking up to 24, and with a product of 945.
RELATED QUESTIONS
If the sum of first four terms of an arithmetic sequence is 16 and their product 105 find (answered by Edwin McCravy)

Three consecutive terms in an arithmetic sequence is given with a middle one x. The sum... (answered by ikleyn)

1. The sum of 4 integers is 24 and their product is 945. What are those integers? 2.... (answered by CPhill,greenestamps)

The sum of four integers in an A.P. is 24 and their product is 945. Find the... (answered by technotarun)

The sum of four consecutive terms of an A.P. is 24 and there products is 945. Find these... (answered by ikleyn)

An arithmetic sequence of 15 terms has a sum of 3060. The common difference and each... (answered by greenestamps)

The first two terms of an arithmetic sequence are 1/8 and 19/24 . What is the... (answered by ewatrrr)

What is the sum of the arithmetic sequence 5, 11, 17 �, if there are 24... (answered by math-vortex)

The product of the first and the third terms of an arithmetic sequence is 5. If all terms (answered by Edwin McCravy)