Which term of the arithmetic progression 3, 15, 27, 39, …… will be 132 more than its 54th term ?
AP GP
4 Likes

Question

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

KnowledgeBoat · Accepted Answer

A.P. = 3, 15, 27, 39, ...... First term (a) = 3 Common difference (d) = 15 - 3 = 12. By formula, a_n = a + (n - 1)d = 3 + 12(n - 1) = 3 + 12n - 12 = 12n - 9. Let nth term of A.P. be 132 more than 54th term. ⇒ a_n = a₅₄ + 132 ⇒ 12n - 9 = a + (54 - 1)d + 132 ⇒ 12n - 9 = 3 + 53 × 12 + 132 ⇒ 12n - 9 = 3 + 636 + 132 ⇒ 12n - 9 = 771 ⇒ 12n = 771 + 9 ⇒ 12n = 780 ⇒ n = = 65. Hence, 65th term of A.P. is 132 more than 54th term.

Mathematics

Which term of the arithmetic progression 3, 15, 27, 39, …… will be 132 more than its 54th term ?

AP GP

Related Questions

Points A, B and C divide the line segment joining the points D(8, -4) and E(-12, 16) in four equal parts. Find the equation of the line that passes through point A and is perpendicular to DE.

Five cards Ten, Jack, Queen, King and Ace of diamonds are shuffled face downwards. Then one card is picked at random.
(i) What is the probability that the card picked is queen ?
(ii) If a king is drawn first and put aside, what is the probability that the second card picked up is the ace ?