Q. 95.0( 4 Votes )

If the nth term of AP – 9, 7, 5, .... is the same as the nth term of the AP – 15, 12, 9...then find the value of n.

Answer :

We know, nth term of an AP is


an = a + (n – 1)d


First AP:


9, 7, 5, …,


First term, a = 9


Common difference, d = a2 – a = 7 – 9 = –2


Let the nth term be an


Second AP:


15, 12, 9, …,


First term, A = 15


Common difference, D = A2 – A = 12 – 15 = –3


Let the nth term be An


Given,


nth term of first AP = nth term of second AP


an = An


a + (n – 1)d = A + (n – 1)D


9 + (n – 1)(–2) = 15 + (n – 1)(–3)


9 – 2n + 2 = 15 – 3n + 3


n = 7


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