Nth term of an Arithmetic Progression – General Term of Arithmetic Sequence
In previous videos we learnt to find the first terms of an Arithmetic progression. And we are now able to write the Arithmetic Sequence or Arithmetic Progression also if we know the first term (a) and common difference (d).
Here in this lesson, we learn general term for an arithmetic progression. Some time we also call it Nth term formula of Arithmetic Sequence.
We will derive two formula of Nth term of an Arithmetic Progression
i. Nth term of Arithmetic Progression from first term
ii. Nth term of Arithmetic Progression from last term
So please don’t forget to sit with pen and paper.
Let’s start –
Well this is called exactly the general term or nth term of an Arithmetic progression. Nth term = a + (n-1).d Where, a = first term, d = common difference & n = term number General Term of an Arithmetic Progression = First Term + (Term Number – 1) *(Common Difference) Nth term of Arithmetic Progression from End
Let there be an Arithmetic progression with first term a and common d. If there are m term in the A. P. , then ,
Nth term from the end of Arithmetic Progression = (m-n + 1)th term from the beginning
Nth term from the end of Arithmetic Progression = A(m-n+1) i.e. (m-n+1)th term
Nth term from the end of Arithmetic Progression =a + (m – n + 1 – 1).d Nth term from the end of Arithmetic Progression =a +(m-n).d
Also if “l” is the term of an Arithmetic Progression then Nth term from end is the nth term of an Arithmetic progression whose first term is l and common difference is –d.
Nth term from the end of Arithmetic Progression = Last Term + (n-1)(-d) Nth term from the end of Arithmetic Progression = l – (n-1).d
I hope you understand how the formula or general term of the Arithmetic Progression come.