Introduction
It's me again, Hayzeed, the mathematics and electrical courses blogger, today we are continuing the last tutorial which is on Number sequence.
What is the Sum of an AP?
Sum of an AP is the algebraic sum/addition of all the terms in a series.
Considering this as an example, 2,3,4,5, 6
The sum of the series = 2+3 +4+5 +6= 20.
What will you do in case you are given a series with 100terms? Will you be adding it one another?
That will consume your time and you might not end up getting it.
This is where Sum of AP formula comes in.
The sum Sn of an AP can be obtained by multiplying the average of all the terms by the number of terms.
The average of all the terms =(a + l)/2
Wherea is the first term
l is the last term= a +(n-1)d
Now, having known how Sum of AP formula is derived, let's try using the above example.
2,3,4,5 ,6
First term a= 2
Common difference d= 3 -2 = 4 - 3= 1
Number of terms n=5
By substituting the values into the formula.
Hence, the sum of the Series is 20.
Can you see that we got the same answer as the first method used?
If you have any questions, kindly comment here.
To be continued on the next tutorial
While waiting for the next tutorial, solve these exercises and post the answers in the comment sections.
Exercises.
- Find the sum of the first 12 terms of
the series 5, 9, 13, 17, ...- The sum of 7 terms of an AP is 35
and the common difference is 1.2. Determine the 1st term of the series- Find the sum of the first 11 terms of the series
4, 7, 10, 13, ...- Determine the sum of the series 6.5, 8.0, 9.5,
11.0, ... , 32
References
Engineering mathematics by John Bird
