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in Arithmetic Progression by (37.9k points)
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For what value of n, are the nth terms of two APs: 63, 65, 67, ….. and 3, 10, 17,… equal?

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Given : The first A.P. is 63, 65, 67, …… 

where a = 63, d = a2 – a1

⇒ d = 65 – 63 = 2 

and the second A.P. is 3, 10, 17, ……. 

where a = 3; d = a2 – a1 = 10 – 3 = 7 

Suppose the nth terms of the two A.Ps are equal, 

where an = a + (n – 1)d 

⇒ 63 + (n – 1)2 = 3 + (n – 1)7 

⇒ 63 + 2n – 2 = 3 + 7n – 7 

⇒ 61 + 2n = 7n – 4 

⇒ 7n – 2n = 61 + 4 

⇒ 5n = 65 

⇒ n = 65/5 = 13 

∴ 13th terms of the two A.Ps are equal.

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