Question

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

Answer 1

3, 15, 27, 39, ………… a_n = ?, n = ? 

a_n = a₅₄ + 132 

a = 3, d = 15 – 3 = 12 

a_n = a₅₄ + 132 

a_n = a + 53d + 132 

3 + 53(12) + 132 

= 3 + 636 + 132 

∴ a_n = 771 

a_n = a + (n – 1) d = 771 

= 3 + (n – 1)12 = 771 

3 + 12n — 12 = 771 

12n – 9 = 771 

12n = 771 + 9 

12n = 780 

∴ n = \(\frac{780}{12}\)

∴ n = 65. 

∴ 65^th term is 132 more than its 54^th term.