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Finding the Term Number Using Nth term Formula of Arithmetic SequencesItsMyAcademy.com

Finding the Term Number Using Nth term Formula of Arithmetic Sequences

Finding the Term Number Using Nth term Formula of Arithmetic Sequences

In previous lesson we learn to find the total number of terms of an Arithmetic Progression. I hope you are good in finding total number of terms of an AP too.

Now in this lesson we are going to learn “how to find the term number (n) of an Arithmetic Progression”. To find the term number we need to apply the nth term formula or general term of arithmetic sequence in various ways depending upon the situation.

So let’s begin our lesson, hope you keep the pen and notebook with you.

So how was it?

In this problem we were given the 3rd term and 9th term of Arithmetic Progression and we need to find that which term of the AP is Zero (0).

Steps

  1. First we need to find the first term & Last term of Arithmetic progression.

  2. Apply the nth term formula of AP in 3rd term using n=3 you will get a relation.

  3. Apply the nth term formula of AP in 9th term using n =9, you will get another relation use the information got on first second step.

  4. You will now found the first term and common difference of arithmetic progression,

  5. Apply the nth term formula for zero, you don’t know n = ?.  Use first term, common difference and nth term = 0 , you will get the value of term number (n).

  6. N is the required term number.

Like this you can solve thousands of problems based on this nth term formula of AP. Here are few problems based on nth term of AP, hope you will try these all. It will really make you smart in nth term of AP related problems.

Q1. The 6th term and 17th term of an A.P. are 19 & 41 respectively. Find the 40th term.  (Answer = 87)

Q2. If 9th term of an A.P. is 0, prove that its 29th term is double the 19th term.

Q3. If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 29th term of the arithmetic progression is zero (0).

Q4. If 10th and 18th terms of an A.P. are 41 and 73 respectively, find 26th term. (Answer =105)

Q5. In certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.

Q6. If (m+1)th term of an Arithmetic progression is twice the (n+1)th term prove that (3m +1)the term is twice the (m + n +1)th term.

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