(9) Find n so that the nth terms of the following two A.P’s are the same

1 , 7 ,13 ,19, ………………. and 100 , 95 , 90 ,………..

Solution:

tn = a + (n - 1) d

nth term of the first sequence

a = 1   d = t₂-t₁

             = 7-1

          d = 6

 tn = 1 + (n-1) 6

 tn = 1 + 6 n – 6

 tn = 6 n – 5   -----(1)

nth term of the second sequence

a = 100   d = t₂-t₁

               = 95 - 100

              d = -5

 tn = 100 + (n-1) (-5)

 tn = 100 - 5 n + 5

 tn = 105 - 5 n   -----(2)

(1) = (2)

6 n – 5 = 105 – 5 n

6 n + 5 n = 105 + 5

11 n = 110

     n =110/11

     n = 11

Therefore 11th terms of the given sequence are equal.