Answer:
The terms of the sequence are x=5 and a=2:
[tex] x + (x + a) + (x + 2a) = 21 [/tex] → [tex] 5 + (5 + 2) + (5 +2*2) = 21 [/tex]
[tex] x*(x + a)*(x + 2a) = 315 [/tex] → [tex] 5*(5 + 2)*(5 + 2*2) = 315 [/tex]
Step-by-step explanation:
We can find the terms of the following sequence:
[tex] x + (x + a) + (x + 2a) = 21 [/tex]
[tex] 3x + 3a = 21 [/tex]
[tex] x + a = 7 [/tex] (1)
The product of that sequence is:
[tex] x*(x + a)*(x + 2a) = 315 [/tex] (2)
Solving equation (1) for x:
[tex] x = 7 - a [/tex] (3)
And by entering (3) into (2):
[tex] (7 - a)*(7 - a + a)*(7 - a + 2a) = 315 [/tex]
[tex] 7*(7^{2} - a^{2}) = 315 [/tex]
[tex] 343 - 7a^{2} = 315 [/tex]
[tex] a = 2 [/tex]
Now, by entering "a" into equation (3):
[tex] x = 7 - 2 = 5 [/tex]
Therefore, the terms of the sequence are x=5 and a=2.
I hope it helps you!
