Arithmetic Sequence

Sequence: -13 -10 -7 – ….. +62      Determine the sum of the arithmetic sequence

62 = -13 + (n-1) (3)

+13    +13       —–> 75 = (n-1) (3) —–> \frac{75}{3} = (n-1) (\frac{3}{3}) ——-> 25=n-1  =    n = 26

/prt 2   S_{26} =  \frac{26}{2} (-13+62)   —–>   S_{26} = 13 (49)    —->    S_{26} = 637

 

Week 2 Convergent / Divergent

Convergent – Where an infinite geometric series that’s sum gets so small it is almost hardly changing the sum. There are two types of infinite geometric convergent series; the first series gets mutiplied by a number less than one, and gradually getting smaller and smaller, but never reaching 0. The second series, R is less than 0 but greater than -1, and makes the series gradually smaller almost reaching 0 dipping up and below the positive and negitive line. Convergent is easy to calculate, and can be using S\frac{a}{1 - r}.

Ex: 2 + 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8}

——>   S\frac{2}{1-1/2}    =     S\frac{2}{1/2} = 4 ——->  S = 4

Divergent – Is the opposite of Convergent, divergent is an infinte geometric series that increases and becomes larger, so large that it becomes almost impossible to find the sum of the infinite series. Just like Convergent, there are two types of Divergent series that can apear; first is a series that increases constanly upward positively being mutiplied by a number grater than 1 2 + 4 + 8 + 16 + 32 + 64….; the second is one that dips into the red when multiplied by a number less than -1. 2 – 8 + 32 – 128 + 512….. It is impossible to calculate a infinite divergent geometric series, and can’t be used by the equation S\frac{a}{1 - r}.

My Arithmetic Sequence

Sequence: 31 + 35 + 39 + 43…..       Find t_{50} & S_{50}

t_n= t_1+(n-1)(d)

Answer/ t_{50} = 31+ (50-1)(4)

=  t_{50} = 31+ (49)(4)

=  t_{50} = 31+ 196   =  t_{50} = 227

——-> S_{50}\frac{50}{2} (31+227)

=   S_{50} = 25 (258)   —>   S_{50} = 6450