A term is any distinct quantity, fraction or proportion in a sequence or series. In exercise 1, find the value of the term indicated in ( ). To do this, use the formula given for each problem. Every number sequence has its own unique formula for finding the term.

Example:

If T_n = 9n - 7 then find T₇₈

T₇₈ = (9 x 78) - 7
       = 702 - 7
       = 695

a = the first term (this is the very first term in an arithmetic progression)
d = the common difference (common difference is the difference between the first term and the second term)

We use the formula T_n = a + (n - 1)d to find the value of any term in a number sequence (A.P.)

To solve the problems in exercise 2, find the value of a and d, then use the formula
T_n = a + (n - 1)d   to work out the answer.

Example:

Find the 20^th term of the sequence 2, 7, 12, 17,...

T_n ...= a + (n - 1)d          a = 2  (2 is the very first term in the number sequence above)
T₂₀= 2 + 19(5)            d = 5  (5 is the common difference between 2 and 7, 7and 12, 12 and 17, etc.)
       = 97

= a + (n - 1)d After finding the product, use the formula S_n = to find the answer. This method is very useful, when finding the sum of many terms.

S = the sum of

n = number of terms

Example:

Find the sum of the following A.P.

S₁₀       a = 1, d = 1

l = a + (n - 1)d
l = 1 + (10 - 1)1
l = 1 + 9 = 10
l = 10

S_n =

.= = 55

Answer = 55

V = Volume
π = pi (3.14) 
r = radius
h = height
Example:                              

A can shaped like a cylinder has a height of 4 cm and a radius of 1.5 cm.
Find the volume of the can.

V = 3.14 x 1.5² x 4
   = 3.14 x 2.25 x 4
   = 7.065 x 4
   = 28.26

When working out the square root of a number it is sometimes necessary to check your answer for accuracy by multiplying the answer by itself. This should come close to the number that was originally calculated.
E.g. the square root of 9 is 3, because 3 x 3= 9, the square root of 25 is 5, because 5 x 5 = 25

To find the square root of any number, follow the steps below...

We will use an example to explain the steps, the rules apply for all numbers.

Place the decimal point behind the number (27)  

Place an amount of zeros in pairs behind the decimal point.    

Remember the more pairs of zeros, the more accurate the answer.

Calculate a number, when multiplied by itself comes close or equal to the number (27) to be calculated. (In this case 5)  Place the  number (5) before the decimal point on top of the square root sign and the result of that number  (which is 25) underneath the number being calculated (27) and subtract it (25) from the number being calculated.(27)
5 x 5 = 25   

Bring down the first two zeros and place them behind the result of the subtraction, (which is 2). Double the number (5)    and place it near the next number down (200). See example...
5 + 5 = 10 

Determine the biggest number placing it behind the number (in this case 10) multiply the total of that number (101) by the number placed behind (10) (in this case 1) remember it must give a result less than or equal to the number being matched (200 in this case). The number you wrote next to the (10) (1), you also write above the last zero which you brought down. Repeat the above steps until you have completed the problem. See example below.

1 x 101 = 101, 9 x 1029 = 9261, 6 x 10386 = 62316    

The side opposite the square of any right angle triangle is called the hypotenuse. To find the hypotenuse, use the formula , where c = the hypotenuse, a = the base of the triangle and b = the height of the triangle. The square is the 90 deg angle in the triangle.

Example:

A right angle triangle has a height of 5 cm and a base of 3 cm, find the hypotenuse.

(note: this answer is rounded to the nearest hundredth)