Question

Which term of the arithmetic progression 8,14,20,26,... will be72 more than its 41th term?

Answer 1

answer : 53rd term of the arithmetic progression will be 72 more than 41th term.

arithmetic progression is..

8 , 14 , 20 , 26 ......

first term , a = 8

common difference, d = 14 - 8 = 6

let nth term of given ap will be 72 more than its 41th term.

i.e., Tn = 72 + T₄₁

⇒a + (n - 1)d = 72 + a + (41 - 1)d

⇒(n - 1) × 6 = 72 + 40 × 6

⇒n - 1 = 12 + 40

⇒n = 1 + 12 + 40 = 53

hence 53rd term of the arithmetic progression will be 72 more than 41th term.

53rd term, T₅₃ = a + (53 - 1)d = 8 + 52 × 6

= 8 + 312 = 320