1.

For what value of n are the nth terms of the following two APs the same 13, 19, 25, ... and 69, 68, 67, ...? Also, find this term.​

Answer»

➝ Given :-

  1. Ap : 13, 19, 25,....
  2. Ap : 69, 68, 67,....

➝ To find :-

  • term of the Ap

➝ Solution :-

Let nth terms of the given progressions be t and T respectively.

➛ The first AP is 13, 19, 25, ....

Let its first term be a and common difference be d. Then,

→ a = 13

→ d = (19-13) = 6.

So, its nth term is given by

↪ t= a+(n-1) d

↪ t = 13+ (n - 1) × 6

↪ t = 6n +7

_____________

➛ The second AP is 69,68, 67, ....

Let its first term be A and common difference be D. Then,

→ A = 69

→ D = (68-69) = -1.

So, it nth term is given by

↪T = A + (n - 1) ×D

↪T = 69+ (n - 1) ×(-1)

↪ T = 70 - n

Now, t = T = 6n + 7 = 70 – n

7n = 63 → n = 9.

Hence, the 9TH term of each AP is the same.

This term = 70 - 9 = 61 [ T = (70 - n)].


Discussion

No Comment Found

Related InterviewSolutions