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Arithmetic Progression Part 1
Posted Date: 14 May 2008 Resource Type: Articles/Knowledge Sharing Category: Education
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Posted By: mark richards Member Level: Silver
Rating:  Points: 4
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So far we have done Geometric Progression, now we are going to look at Arithmetic Progression. Arithmetic Progression deals with reducing or increasing a start number by a fixed value or adding a series of consecutive numbers. There are two popular aspects on Arithmetic Progression but in this post we will look at only one.
First I am going to look at the reducing/increasing aspect of this topic. A.P. questions are well disguised in the S.A.T but it is very easy to identify it by remembering the principle form they appear by. As long as you can identify 3 items in the question, then you will know it is an A.P. question. Look for:
? A start value.
? The number of terms, ‘n’ (e.g. the number of years).
? A fixed number which the start value is reducing/increasing by.
When you find all 3 items in a question it is revealed as an A.P. now let’s look at the A.P. formula. In the A.P. there are 2 useful formulae (also in the G.P. there are 3 but only on is useful in the S.A.T).
Now we are going to look at the first A.P. formula in this post. The first formula is called the ‘n’ term formula.
a + (n - 1) d
the ‘n’ term formula gives the value of the ‘nth term’. The ‘nth’ term means the value of the number you are asked to solve for. Let’s look at an example to clear all confusion.
E.g. A bag contains 1178 marbles. If 27 people, each having bags which can hold a maximum of 8 marbles, how many marbles remained in the bag?
Method 1:
8 x 27 = 216
1178 – 216 = 962
Therefore 962 marbles remained in the bag.
Second method:
a = 1178, n = 28, d = - 8
(NOTE: n equals 28 because n is referring to the number of bags involved and not the number of people involved and d equals – 8 because it is reducing by 8!)
Using the A.P. formula
1178 + (28 – 1)(- 8) = 962
you may have said that this question is easier to be done the first way, yes that’s true, but what if the same exact question came this way instead?
E.g. A bag contains 1178 marbles. It is to be shared in groups of 8 so that there are 962 marbles remaining in the bag. How many bags are needed?
Wouldn’t you use the formula in this case? The formula is useful in some cases; it is up to you to determine which way easier and less time is consumed for you. By manipulating the A.P. formula you can solve for ‘n’. That concludes A.P. part 1; in my other post I will show you the second useful A.P. formula.
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