The question is:

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> Let $a,a+d,a+2d,\cdots ,a+(n-1)d$ be an arithmetic sequence. If the sum of the first, third, fifth, and so on up to the last term is $320$, and the sum of the first, fourth, seventh, and so on up to the last term is $224$, then what is the sum of the entire sequence?
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My attempt was to write the two equations that was given:
$$\left\lfloor\frac{n+1}{2}\right\rfloor a+2\left\lfloor\frac{n-1}{2}\right\rfloor d=320$$
$$\left\lfloor\frac{n+1}{3}\right\rfloor a+3\left\lfloor\frac{n-1}{3}\right\rfloor d=224$$

The expression we want to find the value of is
$$na+nd\frac{n-1}{2}$$

From there I'm stuck. You can't solve the system of two equations above, since there are three variables, so you have to somehow operate between them to reach the third equation. Any suggestions?

I remember seeing this problem somewhere, but I forgot where. If there are any mistakes in the problem, then swtich the "$320$" and the "$224$" in the equations above.

Thanks for your help!