The fifth and and the fiftieth terms of an arithmetic sequence are 3 and 30, respectively. Find the sum of the first 10 terms.
Let be the first term of the sequence and let be the difference between terms. We know that and .
Therefore we can deduce that since the terms are in arithmetic progression we must have that and .
We know the values of and , so we arrive at
Two equations in two unknowns, which I'm sure you can solve. Once you solve you will have and and you should know where to go from there. Good luck.