1. ## arithmetic series

The fifth and and the fiftieth terms of an arithmetic sequence are 3 and 30, respectively. Find the sum of the first 10 terms.

2. Originally Posted by pacman
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 $\displaystyle a_1$ be the first term of the sequence and let $\displaystyle d$ be the difference between terms. We know that $\displaystyle a_5 = 3$ and $\displaystyle a_{15} = 30$.

Therefore we can deduce that since the terms are in arithmetic progression we must have that $\displaystyle a_5 = a_1 + 4d$ and $\displaystyle a_{15} = a_1 + 14d$ .

We know the values of $\displaystyle a_5$ and $\displaystyle a_{15}$, so we arrive at

$\displaystyle a_1 + 4d = 3$
$\displaystyle a_1 + 14d = 30$

Two equations in two unknowns, which I'm sure you can solve. Once you solve you will have $\displaystyle a_1$ and $\displaystyle d,$ and you should know where to go from there. Good luck.

3. Pomp, excuse me, it is fiftieth not fifteenth. Thanks for your reply, i know now how to continue