Q17 of 176 Page 8

For what value of n are the nth term of the following two A.P's the same. Also find this term

13, 19, 25, ... and 69, 68, 67, ...

1st AP = 13, 19, 25, …


Here, a = 13, d = 19 – 13 = 6


and 2nd AP = 69, 68, 67, …


Here, a = 69, d = 68 – 69 = –1


According to the question,


13 + (n – 1)6 = 69 + (n – 1)(–1)


⇒ 13 + 6n – 6 = 69 – n + 1


⇒ 7 + 6n = 70 – n


⇒ 6n + n = 70 – 7


⇒ 7n = 63


⇒ n = 9


9th term of the given AP’s are same.


Now, we will find the 9th term


We have,


an = a + (n – 1)d


a9 = 13 + (9 – 1)6


a9 = 13 + 8 × 6


a9 = 13 + 48


a9 = 61


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For what value of n are the nth term of the following two A.P's the same. Also find this term

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