# Explicit Formulas for Sequences

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• July 21st 2009, 08:38 PM
WeezerFan21
Explicit Formulas for Sequences
Hey, I have a problem in my book for Algebra 2. It's about explicit formulas for sequences. There was one question that said:

"a. Draw the next term in the sequence"

The sequence was a bunch of dots, the 1st one had one dot, the second one had four dots, the third one had nine dots, and the fourth one had 16 dots.

For the next term in the sequence, I drew 25 dots. I am assuming that I am correct, since from the first term, they added three, then they added five, then they added seven.

Here is where I am lost... part b.

It says "Give a formula for Sn, the number of dots in the nth term."

Does anyone know how to give this formula? Thanks a lot. If I am being too confusing, please let me know.
• July 21st 2009, 08:41 PM
Kasper
Quote:

Originally Posted by WeezerFan21
Hey, I have a problem in my book for Algebra 2. It's about explicit formulas for sequences. There was one question that said:

"a. Draw the next term in the sequence"

The sequence was a bunch of dots, the 1st one had one dot, the second one had four dots, the third one had nine dots, and the fourth one had 16 dots.

For the next term in the sequence, I drew 25 dots. I am assuming that I am correct, since from the first term, they added three, then they added five, then they added seven.

Here is where I am lost... part b.

It says "Give a formula for Sn, the number of dots in the nth term."

Does anyone know how to give this formula? Thanks a lot. If I am being too confusing, please let me know.

Another way to look at this sequence is using the formula $S_{n}=n^2$.

$S_{1}=1^2=1$

$S_{2}=2^2=4$

$S_{3}=3^2=9$

$
S_{4}=4^2=16$

$S_{5}=5^2=25$

Does this help?
• July 21st 2009, 08:47 PM
WeezerFan21
Thank you! I appreciate this very much.