why is this a geometric series? why is r = -5/4? putting it step by step would be nice, thank you in advance!
-2+ 5/2 - 25/8 + 125/32 ...
2006-10-02 12:50:09 · 2 answers · asked by Anonymous in Education & Reference ➔ Homework Help
It is a geometric series because each term is found by multiplying the previous term by a number, r (an arithmetic series is where a number, d, is ADDED to the previous term). So you will notice that 5/2 is -2*-5/4 and that -25/8 is 5/2*-5/4, etc.
R stands for ratio and is what you multiply each term by to get the next term.
2006-10-02 12:59:02 · answer #1 · answered by comeagain 2 · 0⤊ 0⤋
A geometric series consists of a series of terms with a common ratio. In this case, you multiply each term by-5/4 to get the next term. Try it. Remember minus times minus is plus. -2x-5/4=+5/2, +5/2x-5/4=-25/8 and so on. An arithmetic series has a common difference, not ratio, so 1+.9+.8+.7+.6... is an arithmetic series.
2006-10-02 20:03:18 · answer #2 · answered by zee_prime 6 · 0⤊ 0⤋