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Sinethemba
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- Mathematics
Mechanical Engineering Technician offering maths lessons in Grade 12 I live in East London
- Mathematics
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About Sinethemba
I'm a Mechanical Engineering Technician I understand grade 12 maths chapters very well which are Patterns, Sequences and Series
Functions and Interverse Functions
Exponential and Logarithmic Functions
Finance, Growth and Decay
Trigonometry: Compound and Double Angle Identities
Trigonometry: Problem Solving in Two and Three Dimentions
Polynomials
Differential Calculus
Analytical Geometry
Euclidean Geometry
Statistics
Counting Principles and Probability
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I want students to understand the basics first eg:Unit 1: Arithmetic sequences
We define an arithmetic sequence as follows
a , a+d; a+2d; a+3d; a+4d; a+(n-1)d
a the value of the first term
d is the common difference between terms, d=t2-t1=t3-t2=tn-tn-1
Tn is the value of the term position n, so Tn=a+(n-1)d
n is the position of a term and can only be positive whole number, also known as a natural number
Consider the arithmetic sequence 3; 7; 11;15;…….99
T1=3, T2=7, T3=11
d1=T2-T1=7-3=4 , d2=T3-T2=11-7=4, d3=T4-T3=15-11=4
Since d1=d2=d3 we have a common difference of 4
The first term is given by a=3 and the common difference is given by d=4
We use a and d to determine the nth term formula in the sequence
Tn=a+(n-1)d
Tn=3+(n-1)4
Tn=3+4n-4
Tn=4n-1
To prove that the formula is correct, you can check the formula by substituting n=1 to obtain the value of T1 and n=2 to obtain the value of T2 and so on
If n =1, then T1=4(1)-1=3
If n=2, then T2=4(2)-1=7
If n=3, then T3=4(3)-1=11
Tn=4n-1 is a correct formula and can be used to determine the position of any term in the sequence
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