Before starting this section, it is recommended you have atleast basic
understanding of Number classification, intergers, multipying, dividing,
adding, substracting integers and fractions, Order of Operations (BOMDAS
or PEMDAS), Factoring.
Difference, sum, product and quotient/ratio
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Difference, sum, product and quotient/ratio
To understand the difference between a linear sequence, quadratic sequence, geometric sequence and series,
one needs to know what is the difference and quotient/ratio.
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Difference, sum, product and quotient
Sum: 6 + 2 = 8
Difference: 6 - 2 = 4
Product: 6 * 2 = 12
Quotient/Ratio: 6 / 2 = 3
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Arithmetic sequence
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Arithmetic sequence
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
And it is the most basic type of all sequences.
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Arithmetic sequence
Finding the 5th term value: Tn = a1 + d(n - 1)
Where:
a1 is the first term
d is the common difference
n is the nth term
Tn is the nth term value
Then, find the difference of the first differences:
21 - 23 = -2
19 - 21 = -2
Find a by 2a = the 2nd difference
2a = -2
2a/2 = -2/2
Therefore, a = -1
Find b by 3a + b = the first value of the first differences
3a + b = 23
3(-1) + b = 23
-3 + b = 23
b = 23 + 3
b = 26
Last but not least, find c by a + b + c = the first value of the sequence
a + b + c = -145
-1 + 26 + c = -144
25 + c = -145
c = -170
Therefore, the quadratic equation for this sequence is:
Tn=-1n2+26n-170
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Given the quadratic pattern: 0; 0; 0; 0; y; ... What is the value of the y term?
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Chances: 2
You get two chances per question.
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What is the formula of the nth term of the pattern ?
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Chances: 3
You get a maximum of three chances for this question.
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A new pattern is formed by adding 0 to each value of the pattern, what is the formula of the new pattern ?
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Chances: 3
You get a maximum of three chances for this question.
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What is the value of the newly formed sequence nth term, if nth term is 0?
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Chances: 3
You get a maximum of three chances for this question.
The first question you got 0/2
The second question you got 0/3
The third question you got 0/3
The forth question you got 0/2
Your total is therefore, 0/9.
Percentage
%
A Message here
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Geometric sequences and series
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Geometric sequences and series
Understand what is a geometric sequence, geometric series, finding their nth terms, finding the arithmetic and geometric mean.
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Geometric sequences and series
Geometric sequences are defined by having a common ratio:
Has an equation of an = a1(r)n - 1
Where:
r is the common ratio.
n is the nth term.
a1 is the first value of the sequence.
an is the value of the nth term.
Finding the 6th term of the sequence: 3; 6; 12; 24; 48; ....
Firstly, find the common ratio:
6/3 = 2;
12/6 = 2;
24/12 = 2;
48/12 = 2
Therefore, the common ration is 2.
Substitute everything into the equation.
an = a1(r)n - 1 a(6) = 3(2)6 - 1 a(6) = 3(2)5 a(6) = 3(32) a(6) = 96
Therefore, the 6th term is 92.
Geometry series is the sum of a geometric sequence:
There are two geometric series in a geometric sequence:
1. Finite series, which can be identified by the lack of three dots at the end of the series
2. Infinite series, which can be identified by having three dots at the end of the series
Finite Series equation
Sn = a1[1 - rn]/ 1 - r
Find the sum of the following: 100 + 90 + 81 + 72.9 + 65.61 + 59.049.
3; 6; 12; 24; 48.
Sn = a1[1 - rn]/ 1 - r
Sn = 3[1 - 25]/ 1 - 2
Sn = 3[1 - 32]/ 1 - 2
Sn = 3[-31]/ - 1
Sn = [-93]/ - 1
Sn = 93
However, if we made this sequence back to infinite (3; 6; 12; 24; 48;...), you couldn't find the sum.
Because the sum of an infinite geometric sequence can only be found if the common ratio is
less than 1 or greater than -1.
If the ratio of an infinite geometric sequence is between -1 and 1, then you can use:
S∞ = a1/ 1 - r
Finding the geometric sequence mean: MG = √afirst-term x alast-term
E.g. 3; 6; 12; 24; 48.
MG = √a1 x a1 MG = √3 x 48 MG = √144 MG = 12
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Given the geometric series: x + 0 + 0 + 0 + ....
What is the value of x?
Round-off your answer into a whole number.
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Chances: 3
⚠️Roundoff your answer into a whole number.
You get a maximum of three chances for this question.
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Now, what is the value of 0th term?
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Chances: 3
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Using one of the equation used to calculate Geometric series sums, calculate the sum of the following: 0 + 0 + 0 + 0
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Chances: 3
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Using one of the equation used to calculate Geometric series sums, calculate the sum of the following: 0 + 0 + 0 + 0+...
Roundoff into two decimal places.
✔️❌
Chances: 2
⚠️Roundoff into two decimal places.
You get a maximum of two chances for this question.
The first question you got 0/3
The second question you got 0/3
The second question you got 0/3
The second question you got 0/3
Your total is therefore, 0/6.
Percentage
%
A Message here
×
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Solve the following: 0/0 ÷ 0/0
Chances: 1
You get one chance for this question.
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Solve the following: 0/0 + (0)/0
Chances: 2
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Solve the following: 0/0 + 0/0
Chances: 2
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Solve the following: 0/0 - 0/0
Chances: 2
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A a box with a mass of 0kg rests on a flat surface, find the normal acting on the box.
Chances: 2
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Find the static friction of the box, if its coefficient was 0.
Chances: 2
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The box is now pushed horizontal to the right by a force of 0N is moving to the right with an acceleration of 0m/s2, what is the coefficient of the kinetic friction?
Chances: 3
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The box is now pushed at angle of 0° to the right by a force of 0N, Calculate the new normal force.
Chances: 3
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As the box continue to move, what is the acceleration of the box if kinetic friction coeffient was 0.
Chances: 3
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