Q. 114.2( 228 Votes )

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

Answer :

To find : n such that an = a54 + 132
Given:  a = 3, d = 15 – 3 = 12

nth term of an AP is given by:
an = a + (n - 1) d
where,
a = first term of AP
n = no. of terms of AP
d = common difference of AP

54th term can be given as follows:

a54 = a + ( 54 - 1)d


     = 3 + 53 x 12


      = 3 + 636
= 639

In question we have to find the term which is 132 more than 639 i.e. 771
Now an = 771, n = ?
Again applying the formula of nth term

      771 = a + (n – 1)d


      771 = 3 + (n -1)12


      (n – 1)12 = 771 – 3 = 768


      n - 1 = 768/12
 
      n – 1 = 64


     n = 65


Thus, the required term is 65th term.

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