Mathematics: Post your doubts here!

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My Name

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Evangeline

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queen of the legend said:
anyone how to work the sequences., coz the questions on it are damn hard !
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Nth Term

The rule for finding any term is called the nth term.

For example:Given the sequence 6,10,14,18,……

a) Find the nth termb) the 20th termc)If the nth term is 42, what is the value of n?

We look at the differences between each term
6 10 14 18
\ _/\_ /\_ /
4 4 4The difference is four
The general formula for the nth term is:
nth term = a + (n-1)dwhere a = the first term =6
n = the number of the term
D = the difference = 4
For this sequencenth term = 6 + (n-1)4
= 6 + 4n - 4
= 2 + 4n
We can now use this formula to work out the value of any term in the sequence.
b)20th term =
2 + 4 x 20
= 82because n = 20
c)nth term = 42
42 = 2 + 4n
40 = 4n
n = 10
So the 10th term is 42.

This formula will work for any linear sequence. In a linear sequence the difference is constant. 4 in the sequence above.


If quadratic
In this type the first difference is not constant. The second difference gives a constant.

For example:3,8,15,24,36……… is a sequence. 3 8 15 24 35
\_/\_ /\_ /\_ /
5 7 9 11
\_ /\_ /\_ /
2 2 21st difference

2nd difference

This is a quadratic sequence as the 2nd difference is a constant (in this case, 2.)

The general formula for a quadratic is:

nth term = a + (n-1)d1 + ½(n-1)(n-2)d2Where a = 1st term
d1= 1st difference

d2= 2nd difference

= 3= 5= 2 nth term = 3 + (n-1)5 + ½ (n-1)(n-2)2
= 3 + 5n - 5 +n2 -3n + 2
= n2 +2n
We can use this to find the 100th term:
100th term = 1002 + 200
= 10200
Provided that the second difference is a constant we can use this method for any quadratic sequence.
 
Bloodserpent

Bloodserpent

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My Name said:
http://papers.xtremepapers.com/CIE/Cambridge IGCSE/Mathematics (0580)/0580_s10_qp_23.pdf
question 23 part b

who ever answers plz give me a brief note
i hate bearings and my concept is not clear in this part of trig!
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23 isn't bearings :|

To find the inverse matrix of
(3 -1)
(-2 2)

1/((3x2)-(-1x2)) *Here*

*This below*
(2_1)
(2_3)

1/4 (2_1)
.......(2_3)
^^^^^^ is the answer

How?

use the formula

1/(ad-bc) . (d..-b)
..................(-c ..a)
Invert the signs of any numbers in position b and c and switch the positions of a and d

Imagine there are no dots.. cant use lots of spaces here..
 
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