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

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

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

Answer»

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.