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,… .

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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