SOLUTION: identify the following series as arithmetic , geometric , or neither. 1. 3a + 3a^2 + 3a^3 + 3a^4 +...+ 3a^n +... 2. -3+3-3+3-3+3.... 3. n=1 (3+na) >> above this is a si

Algebra ->  Sequences-and-series -> SOLUTION: identify the following series as arithmetic , geometric , or neither. 1. 3a + 3a^2 + 3a^3 + 3a^4 +...+ 3a^n +... 2. -3+3-3+3-3+3.... 3. n=1 (3+na) >> above this is a si      Log On


   

Question 446591: identify the following series as arithmetic , geometric , or neither.
1. 3a + 3a^2 + 3a^3 + 3a^4 +...+ 3a^n +...
2. -3+3-3+3-3+3....
3. n=1 (3+na) >> above this is a sideways 8 and a sideways M <<<
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
1. Geometric, common ratio is a.

2. Geometric, common ratio is -1. This series does not converge though, the ratio has to be strictly between -1 and 1 for the series to converge.

3. I presume you mean

where is the infinity symbol and is the Greek uppercase letter sigma. If a is a constant, then the series is

, in which the sequence determined is arithmetic with common difference n.