Find a formula for the sequence....

Dec 2009
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The two questions are here, they're probably easy but I'm having a brain freeze lol

http://img29.imageshack.us/img29/5626/file.png

The 4(c) sequence is 5, 7, 9, 11....
The 4(d) sequence is 5, -10, 20, -40.....
Hi brumby_3,


1st one

\(\displaystyle 5,\ 7,\ 9,\ 11,......\)

is an ARITHMETIC SEQUENCE.

\(\displaystyle T_1=5,\ T_2=5+(1)2,\ T_3=5+(2)2,\ T_4=5+(3)2,\ T_5=5+4(2)...\)

\(\displaystyle T_n=5+(n-1)2\)

To sum all the terms of the sequence, the sum is

\(\displaystyle S_n=\frac{T_1+T_n}{2}(n)\)

which is the average value multiplied by the number of terms.

\(\displaystyle S_n=\frac{5+5+(n-1)2}{2}(n)\)


2nd one

\(\displaystyle 5,\ -10,\ 20,\ -40,.....\)

The next term is the previous one multiplied by \(\displaystyle -2\)

This is a GEOMETRIC SEQUENCE.

\(\displaystyle T_1=5,\ T_2=(-2)5,\ T_3=(-2)^25,\ T_4=(-2)^35,...\)

\(\displaystyle T_n=5(-2)^{n-1}\)

The sum of these terms is

\(\displaystyle S_n=\frac{5\left(1-(-2)^{n}\right)}{1-(-2)}\)

which is \(\displaystyle \frac{a\left(1-r^n\right)}{1-r}\)

where "a"=1st term, "r"=common ratio.
 
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