Chad's Math Tutorial Site

Chapter 12

Arithmetic Sequences and Series

Section 1

important information and formulas

Quote:

You have to do your own growing no matter how tall your grandfather was.
--Abraham Lincoln (1809-1865)

This means that no matter how successful your grandfather, father, mother, or grandmother was you need to become your own person having perseverance and integrity.

To find  the nth term in a sequence: A_n= A₁ + (n-1)d

Arithmetic Series: A₁, A₁+D,A₁+2D...

Sum of a Arithmetic Sequence: S_n= ⁿ/₂ (A₁+A_n)

A_n = any number in a series or sequence

A₁ = the first number in the series or sequence

n = the number of terms in the series or sequence

d = the difference between the terms in the series or sequence

Here is an example problem:

find the next 4 terms of this sequence

-4+1+6....

find the difference between the terms then use the formula above titled arithmetic sequence

1-(-4)=5

-4+1+6+11+16+21+26

Example⁺

^{find the sum of the same series in the about problem}

S_n= ⁿ/₂ (A₁+A_n)

S₇ = 7/2 (-4+26) = 3.5 (22) =77

Example⁺⁺

Using new information find the 685th term in the series.

A₁=6 n=685 d=4

A_n = A₁ + (n-1)d

A_n=6 + (685-1)4

For additional help visit the website below

Http://mathworld.pdox.net/math/a/a351.htm

Character Education Trait

WORD PROBLEM

Imagine this, what if I told you that I will give you 10 dollars on January 1st and I would add 10 more dollars to it everyday until December 31st OR I will give you 3500 dollars on December 31^st? With the above formulas find out which way will you make more money.

A_{365= 10+(365-1)10     =10+3640   =$3650.00}

_{Now as you have scene with these formulas you can really make money. These formulas let you make the intelligent decision of taking 10 dollars a day, to make more money.}

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