1. ## Sequences and Series Help (Grade 11)

Hi guys,

I have a math assignment here dealing with geometric series/sequences, arithmetic series/sequences, and the recursion formula. The problem is that I don't know which formula applies to which question!

If you could, a detailed explanation would be really wonderful.

Here are the questions:

1. Find $\displaystyle tn$ and $\displaystyle t11$ for the sequence $\displaystyle 6x,12x^2, 24^3...$
(For this one, I use the geometric sequence, right?)

2. Find $\displaystyle s31$ for $\displaystyle 36+34+32+...$

3. Each year, for 8 years, the population of a city increased by 3.5% of its value in the previous year. If the initial population was 320 000, what was its population by the end of the 8th year?

4. If a sequence is determined by $\displaystyle f(x) = 6^x-1$ where $\displaystyle x$ is a natural number, find the sum of the first 15 terms.

Of course I don't expect anyone to help me with all of them, but even if you helped me figure out which formula to use for any of them, I would be really grateful!

Thank you so much in advance!

2. 1. You see that the number double every time so you will have something like $\displaystyle 2^n$ As for the x you see that the exponent also increase by 1 each time so that you have $\displaystyle x^n$
2. The term decrease by 2 every time $\displaystyle i_n = 38 - n$ You want $\displaystyle \sum_{n=1}^{31} 38 -n$ remember that $\displaystyle \sum_{n=1}^i n = \frac{i^2+i}{2}$.
3. $\displaystyle P = P + 0.035 P = 1.035 P$ That's for one year, the next year $\displaystyle 1.035 \cdot (1.035 \cdot P) = 1.035^2 P$After n years $\displaystyle P_{tot} = 1.035^n P$
4. Use $\displaystyle \sum_{i=0}^n 6^i = \frac{1-6^{n+1}}{1-6}$ Decompose the sum and use also $\displaystyle \sum_{i=0}^n 1 = n$

3. Thank you very much for your help, vincisonfire.