Arithmetic Progression : Part 3

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This post will be the last part of arithmetic progression, which is finding the sum of the n^th terms.

Firstly, what does it mean by sum of n^th terms?

In simple explanation, if we have an arithmetic sequence such as

2, 5, 8, 11, 14, 17, 20, …

Question : Find the sum of the first 6 terms.

The question actually asks you to find….

The sum of     2 + 5 + 8 + 11 + 14 + 17

                       = 57

Very simple right?

But, because it is a very special sequence, which have a common difference, then we may apply a formula to find the sum of it.

We will use two formula.

First Formula:  

What is a? Recall from previous lesson:

a is the first term. So a = 2.

Next, what is d ?  d is the common difference, so

                d = 5 - 3 

                   = 2 

What is n? n is number of terms that we want to sum.

From the formula;   S₆ = (6/2) (2(2) + (6-1)3)
                                     = 57

The same answer right? So, if you know the number of terms, the first term, and the common difference, then just use this formula. If you have a few numbers in the list, maybe you can simply list it and sum all of them, but what happen if you have many terms to be added such as 50 terms?

Then this formula can be applied.

Second Formula: 

We can use this formula when we know the last term to be summed. From the example :
the first term a, a= 2. Number of term to be added, n = 6. The 6^th is , l = 17.

so, 

        = 57

So, exactly using all the methods, the answer still the same.
Choose wisely while you want to answer the question.

Good Luck.

Task 1: 
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Next, Try as many as questions you can. You may copy the questions.
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Task 3: 
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Try questions from your module page 7 - 10.  Module
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Task 4:
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#QUIZ 2  code:  828919 . Due date 16 April 2020 before 11.45pm.

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