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

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- Sep 1st 2009, 07:30 PMpacmanarithmetic 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.

- Sep 1st 2009, 07:36 PMpomp
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. - Sep 1st 2009, 10:12 PMpacman
**Pomp**, excuse me, it is**fiftieth**not fifteenth. Thanks for your reply, i know now how to continue