# arithmetic series

• Sep 1st 2009, 07:30 PM
pacman
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.
• Sep 1st 2009, 07:36 PM
pomp
Quote:

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.
• Sep 1st 2009, 10:12 PM
pacman
Pomp, excuse me, it is fiftieth not fifteenth. Thanks for your reply, i know now how to continue