# Sequences/Series Sigma Question

1. Nov 20, 2008

### JBD2

1. The problem statement, all variables and given/known data

If $$\sum_{n=1}^{4}log_{2}x^{n}=80$$, determine the value of x.

2. Relevant equations

$$S_{n} = \frac{a(r^{n}-1)}{r-1}$$

$$S_{n} = \frac{rt_{n}-a}{r-1}$$

3. The attempt at a solution

$$log_{2}1+log_{2}x^{2}+log_{2}x^{6}+log_{2}x^{12}=80$$?

$$log_{2}x^{20} = 80$$

$$2^{80}=x^{20}$$

$$x=16$$

Is this right? Or does x have to be + or - 16 or am I just completely wrong?

Last edited: Nov 20, 2008
2. Nov 20, 2008

### Avodyne

This looks right, assuming that $$log_{2}x^{n}$$ means $$\log_{2}(x^{n})$$ and not $$(\log_{2}x)^n$$.

3. Nov 20, 2008

### JBD2

Ok well I have two more questions, and rather than clutter the board with another post I'll put them here:

Question 2:
1. The problem statement, all variables and given/known data
A new car costs $42 000 and depreciates 20% the first year, then 15% every year after. What is the car worth in 10 years? 3. The attempt at a solution 42 000 + 42 000(0.8) + 33600(0.85) + 33600(0.85)2... I'm not sure if this is right so far, but I'm pretty sure I can separate the 42 000(0.8) and the 33600(0.85) right? What should I do? Question 3: 1. The problem statement, all variables and given/known data In a geometric sequence, t2+t3=60 while t4+t5=1500. Find the first 3 terms. 3. The attempt at a solution Not really sure how to start this one, I think that t4 is equal to 60r and t5 is equal to 60r2, so can I go: 60r + 60r2=1500 and solve for r? If I do this I end up getting $$\frac{-1\pm\sqrt{101}}{2}$$ which I'm sure can't be correct. Last edited: Nov 20, 2008 4. Nov 20, 2008 ### Chaos2009 Well, I don't think your first problem is a series. I think you are making it too hard on yourself. It starts at$42,000, loses 20%, and becomes \$33600 after one year. I don't think you just keep adding them up.

5. Nov 20, 2008

### Avodyne

If you're supposed to add them up, then I want that car!

As for #3, for a geometric series, $$t_n = a\,r^n$$ for some constants a and r. So you have two equations in two unknowns.