Finding the equation of a series

[series001]

Hi guys, can help me solve this series?

S=0,2,6,14,30.... given n=1,2,3,4,5... and d=2

S=0,4,12,28,60.... given n=1,2,3,4,5... and d=3
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d is from 2 onwards

S=?n?d

[zaza]

Look at the differences between successive numbers in both of your series.

[series001]

the difference is p*2+2 where p is the previous number for d=2 and p*2+4 for d=3, but how to build a relation for this?

[zaza]

Perhaps by using a "Sum from 1 to i" of some function? Also, think about powers of 2...

[03myersd]

Its been a long time since I have done this but I seem to remember that you start of by finding how many 'levels' down the difference between two numbers is 1. E.g.

0    2    6    14    30
   2    4    8     16   
      2    4     8...

Then this number is the power of n that you use. Cant remember the rest though. May be way off with this too....

[zaza]

A series is just a way of generating a sequence of numbers. Often, people are concerned with arithmetic or geometric series, where the terms are additive or multiplicative respectively.

Take the first example.

n=1 -> a1 = 0
n=2 -> a2 = 2 = a1 + 2^1
n=3 -> a3 = 6 = a2 + 2^2
n=4 -> a4 = 14 = a3 + 2^3
....


When you have an arithmetic series, you are looking at the difference between each term and the next. In a geometric series you look at the ratio of one term to the next.

Having practically handed you the first one on a plate, you can now write down the general formula (hint: it uses powers of 2) and then have a go at #2, which is pretty much identical. You'll be able to see that for nether of these do you actually need to refer to the previous term.

zaza

[series001]

hmm, i've never thought of using power 2. I'll try work it out. Thx guys.