Question

The sun of the first 3 terms of an arithmetic sequence is 21 while their product is 315 determine these three terms?

Answer 1

Answer:

The terms of the sequence are x=5 and a=2:

$x + (x + a) + (x + 2a) = 21$  →  $5 + (5 + 2) + (5 +2*2) = 21$

$x*(x + a)*(x + 2a) = 315$  →  $5*(5 + 2)*(5 + 2*2) = 315$

Step-by-step explanation:

We can find the terms of the following sequence:

$x + (x + a) + (x + 2a) = 21$

$3x + 3a = 21$      

$x + a = 7$      (1)

The product of that sequence is:

$x*(x + a)*(x + 2a) = 315$    (2)

Solving equation (1) for x:

$x = 7 - a$  (3)

And by entering (3) into (2):

$(7 - a)*(7 - a + a)*(7 - a + 2a) = 315$  

$7*(7^{2} - a^{2}) = 315$  

$343 - 7a^{2} = 315$    

$a = 2$  

Now, by entering "a" into equation (3):

$x = 7 - 2 = 5$  

Therefore, the terms of the sequence are x=5 and a=2.

I hope it helps you!