# Find a formula for the sequence....

#### brumby_3

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.

• brumby_3