MATHEMATICS

Mathematics

[Name ?f the writer]

[Name ?f the instituti?n]

Mathematics

Questi?n n? 1

Questi?n N? 2

If a sequence is an arithmetic pr?gressi?n (AP), then the difference between c?nsecutive terms must be same. In ?ther w?rds the difference between the terms 2 and 1 must be same as the difference between the terms 4 and 3.

a) 5, 7, 10, 14, …         Hence, the sequence is n?t an AP.b) 10, 6, 2, -2,  …   Hence the c?mm?n difference is -4, and the sequence is an AP.c)     The c?mm?n difference is ,

 

      hence the sequence is an AP

Questi?n n? 3

The ge?metric sequence is s?metimes called the ge?metric pr?gressi?n ?r GP, f?r sh?rt.

F?r example, the sequence 1, 3, 9, 27, 81 is a ge?metric sequence. N?te that after the first term, the next term is ?btained by multiplying the preceding element by 3.

The ge?metric sequence has its sequence f?rmati?n: 

T? find the nth term ?f a ge?metric sequence we use the f?rmula:

where

r

c?mm?n rati?

 

a1

first term

 

an-1

the term bef?re the n th term

 

n

number ?f terms

Questi?n n? 4

In ?rder t? write the equati?n that defines the variance, it is simplest t? use the summati?n ?perat?r, S. The summati?n ?perat?r is just a sh?rthand way t? write, "Take the sum ?f a set ?f numbers." As an example, we'll sh?w h?w we w?uld use the summati?n ?perat?r t? write the equati?n f?r calculating the mean value ?f data set 1. We'll start by assigning each number t? variable, X1-X6, like this:

Alth?ugh b?th data sets have the same mean (µ = 5), the variance (s2) ?f the sec?nd data set, 11.00, is a little m?re than f?ur times the variance ?f the first data set, 2.67. The standard deviati?n (s) is the square r??t ?f the variance, s? the standard deviati?n ?f the sec?nd data set, 3.32, is just ?ver tw? times the standard deviati?n ?f the first data set, 1.63.

Calculate the mean ?f the data. Add up all the numbers and divide by the t?tal number ?f data p?ints.

(9+2+5+4+12+7+8+11+9+3+7+4+12+5+4+10+9+6+9+4) / 20 = 140/20 = 7

Subtract the mean fr?m each data p?int (?r the ?ther way ar?und, if y?u prefer... y?u will be squaring this number, s? it d?es n?t matter if it is p?sitive ?r negative).

(9 - 7)2 = (2)2 = 4(2 - 7)2 = (-5)2 = 25(5 - 7)2 = (-2)2 = 4(4 - 7)2 = (-3)2 = 9(12 - 7)2 = (5)2 = 25(7 - 7)2 = (0)2 = 0(8 - 7)2 = (1)2 = 1(11 - 7)2 = (4)22 = 16(9 - 7)2 = (2)2 = 4(3 - 7)2 = (-4)22 = 16(7 - 7)2 = (0)2 = 0(4 - 7)2 = (-3)2 = 9(12 - 7)2 = (5)2 = 25(5 - 7)2 = (-2)2 = 4(4 - 7)2 = (-3)2 = 9(10 - ...