Question

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

Answer 1

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

Answer 2

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.