Q. 143.8( 10 Votes )

If the nth term of the A.P. 9, 7, 5,… is same as the nth term of the A.P. 15, 12, 9 … Find n.

Answer :

Given: nth term of the A.P. 9, 7, 5,… is same as the nth term of the A.P. 15, 12, 9 …


We know, an = a + (n – 1)d where a is first term or a1 and d is common difference and n is any natural number


Let A.P. 9, 7, 5,… has first term a1 and common difference d1


a1 = 9 and a2 = 7


Common difference, d1 = a2 – a1 = 7 – 9 = -2


Now, an = a1 + (n – 1)d1


an = 9 + (n – 1)(-2)


an = 9 – 2n + 2


an = 11 – 2n


Let A.P. 15, 12, 9 … has first term a1 and common difference d1


b1 = 15 and b2 = 12


Common difference, d2 = b2 – b1 = 12 – 15 = -3


Now, bn = b1 + (n – 1)d2


bn = 15 + (n – 1)(-3)


bn = 15 – 3n + 3


bn = 12 – 3n


According to question:


an = bn


11 – 2n = 12 – 3n


3n – 2n = 12 – 11


n = 1


Hence, the value of n is 1


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