Q. 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,… .

Answer :

For first A.P. , first term, a = 1; common difference, d = 7 – 1 = 6


For second A.P, first term, a = 100; common difference , d = 95 – 100 = -5


We know that nth term of A.P. , tn = a + (n – 1) d.


First A.P:


tn1 = 1 + (n – 1) (6)


= 1 + 6n – 6


tn1 = 6n – 5


Second A.P:


tn2 = 100 + (n – 1) (-5)


= 100 – 5n + 5


tn2 = 105 – 5n


Given that nth terms of the two A.P.’s are the same.


tn1 = tn2


6n – 5 = 105 – 5n


6n + 5n = 105 + 5


11n = 110


n = 110/11 = 10


For the nth terms of the two given A.P.’s to be same, the value of n = 10.


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