Q. 19 B4.3( 3 Votes )

Which term of the A.P. 3, 15, 27, 39, ... will be 132 more than its 54th term?

Answer :

Given: 3, 15, 27, 39, …


First we need to calculate 54th term.


We know that


an = a + (n – 1)d


Here, a = 3, d = 15 – 3 = 12 and n = 54


So, a54 = 3 + (54 – 1)12


a54 = 3 + 53 × 12


a54 = 3 + 636


a54 = 639


Now, the term is 132 more than a54 is 132 + 639 = 771


Now,


a + (n – 1)d = 771


3 + (n – 1)12 = 771


3 + 12n – 12 = 771


12n = 771 + 12 – 3


12n = 780


n = 65


Hence, the 65th term is 132 more than the 54th term.


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