Question

Which term of the AP 3, 15, 27, 9, ..... will be 132
mroe than its 54th term?​

Answer 1

Question:-

Which term of the AP 3, 15, 27, 9, ..... will be 132

more than its 54th term?

Solution:-

an = a + ( n − 1 ) d

3 , 15 , 27 , 9

a = 3 ; d = 15 − 3 = 12 ; n = 54

a54 = a + ( n − 1 ) d

= 3 + ( 54 − 1 ) × 12

= 3 + 53 × 12

= 639

That will be 132 more than 54th term.

= 639 + 132 => 771

An = a ( n - 1 ) d

771 = 3( n - 1)12

64 = n - 1

n = 65

Answer 2

Solution:

a = 3
d = 12

Tn = a + (n - 1)d

= 3 + (54 - 1)12

= 3 + (53)12

= 3 + 636

= 639

132 + 639 = 771

We have to find the term of this A.P. which is 771.
Let nth term be 771.

Tn = a + (n - 1)d

771 = 3 + (n - 1) 12

768 = ( n - 1 )12

(n - 1 ) = 768/12

(n - 1) = 64

n = 64 + 1

n = 65

Therefore, 65th term was 132 more than 54th term.

Hope this would help