The pattern is *2 +3 *2 +3 *2 +3 .... 1 *2 = 2 , 2+3 = 5 , 5 *2 = 10, 10 +3 = 13, 13*2 = ?...
Divide by the number of items.
(7+x)+x=15
I did trial and error to get x=4.
Your geometric series starts with 6, and then you get the next term by multiplying the previous one by 1/3. So, the first five terms are
![a_1=6](https://tex.z-dn.net/?f=a_1%3D6)
![a_2=6\cdot\dfrac{1}{3}=2](https://tex.z-dn.net/?f=a_2%3D6%5Ccdot%5Cdfrac%7B1%7D%7B3%7D%3D2)
![a_3=2\cdot\dfrac{1}{3}=\dfrac{2}{3}](https://tex.z-dn.net/?f=a_3%3D2%5Ccdot%5Cdfrac%7B1%7D%7B3%7D%3D%5Cdfrac%7B2%7D%7B3%7D)
![a_4=\dfrac{2}{3}\cdot\dfrac{1}{3}=\dfrac{2}{9}](https://tex.z-dn.net/?f=a_4%3D%5Cdfrac%7B2%7D%7B3%7D%5Ccdot%5Cdfrac%7B1%7D%7B3%7D%3D%5Cdfrac%7B2%7D%7B9%7D)
![a_5=\dfrac{2}{9}\cdot\dfrac{1}{3}=\dfrac{2}{27}](https://tex.z-dn.net/?f=a_5%3D%5Cdfrac%7B2%7D%7B9%7D%5Ccdot%5Cdfrac%7B1%7D%7B3%7D%3D%5Cdfrac%7B2%7D%7B27%7D)
And if we sum them we have
![8+\dfrac{2}{3}+\dfrac{2}{9}+\dfrac{2}{27}=\dfrac{242}{27}](https://tex.z-dn.net/?f=8%2B%5Cdfrac%7B2%7D%7B3%7D%2B%5Cdfrac%7B2%7D%7B9%7D%2B%5Cdfrac%7B2%7D%7B27%7D%3D%5Cdfrac%7B242%7D%7B27%7D)
8585 is odd, so one of the primes is even and the other is odd (otherwise their sum would be even). 2 is the only even prime. Thus, second prime is 8585-2=8583. Their product is 8583*2=<span>17166.</span>