The sum of the first 3 terms of an arithmetic sequence is 21, while their product is 315. determine these 3 terms

Given:

Sum of arithmetic sequence is 21.

Product of arithmetic sequence is 315.

I did a manual computation. Arithmetic sequence means that there is a constant difference between the two consecutive numbers.

x + (x+2) + (x + 2 + 2) = 21

3x + 6 = 21

3x = 21 - 6

3x = 15

x = 15/3

x = 5 1st number

x + 2 = 5 + 2 = 7 2nd number

x + 2 + 2 = 5 + 2 + 2 = 9 3rd number.

5 + 7 + 9 = 21

5 x 7 x 9 = 315

These three terms can be written as a-d, a, a+d

Then (a-d) + a + (a+d) = 21, i. e. 3a=21 and a=7.

So,

7 (7-d) (7+d) = 315

7²-d²=315/7=45

d²=49-45=4

d=2 or d=-2.

Thus, we have terms 5,7,9 or 9,7,5.