This is the Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE
Board.
Here the AP and the last term of AP is given you have to find which term of the AP this must be.
This is the Question Number 11 Exercise 11 A of RS Aggarwal Solution.
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Which term of the AP 5 /6 , 1, 1 1 /6 , 1 1 /3 , ….. is 3?
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AP is 5 /6 , 1, 1 1 /6 , 1 1 /3 , …..
Here,
First term = a = 5/6
Common difference = d = 1 – 5/6 = 1/6
Now: a_n = a + (n – 1)d
3 = 5/6 + (n – 1)1/6
Let nth term is 3
Now, a_n = a + (n-1)d
3 = 5/6 + (n-1)1/6
n -1 = 13
n = 13 + 1 = 14
Therefore, 3 is the 14th term.