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How to find the Number of Terms of an Arithmetic Sequence from Sum of N terms Formula

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Published on Jan 24, 2011

http://ItsMyAcademy.com/arithmetic-se... For Free Complete Video Tutorial on Sequence & Series.
To find the number of terms of an arithmetic sequence using sum of N terms formula , first we have to see what are the given information and what extra we need to find. If there are at least 3 variables given already in questions then we can easily calculate the number of terms of that arithmetic sequences.
To Find the number of terms of an arithmetic sequence we should know the first term, common difference and sum of the series, Or we should know first term, last term and the sum of series.
Then its easy to calculate the number of terms using sum of n terms formula of arithmetic series.

I hope you understand the trick to find the number of terms of an arithmetic sequences.

How to find the Number of Terms of an Arithmetic Sequence from Sum of N terms Formula
In previous video lessons we learned a lot about the sum of arithmetic progression formula.
Now in this video lesson we are going to learn how to find the number of terms in an arithmetic progression using the sum of n term formula.
As we have learned in previous lesson there are two formula for finding the sum of n terms of an Arithmetic progression . But we will use the first one the formula in which first term (a), common difference (d) , number of terms (n) and the sum of sequence are the quantities given below :
Sum of Arithmetic Sequence = [ n {2a + (n-1) d} ] / 2
So how will use it and wil find the term number we will discuss in video. So lets start the lesson. I hope you have the pen and notebook with you.

Great ! So I hope now you understand how to find the term number.
Simply we have to put all the information provided by the question into the formula and solving it result the total number of terms in that arithetmic sequence .
Here are some few exercise please try them once you will get good confidence after this. If you feel any problem then please comment.
Q1. In an Arithmetic progression (A.P.) if first term is 22, the common difference is -4 and sum to n terms is 64, find n? (Ans = 4 or 8)
Q2. How many terms are there in the arithmetic progression whose first term and fifth terms are -14 and 2 respectively and sum of the terms is 40? (Ans = 10)

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