Answer :

Given A.P. is 9, 7, 5….

Whose first tern a = 9


Second term t1 = 7


Third term t3 = 5


Common difference d = t3 – t2 = 5 – 7 = – 2


Another A.P. is 24, 21, 18, . . .


Whose first tern a = 24


Second term t1 = 21


Third term t3 = 18


Common difference d = t3 – t2 = 18 – 21 = – 3


We have been given, nth term of both the A.P. is same


thus, by using nth term of an A.P. formula


tn = a + (n – 1)d


where n = no. of terms


a = first term


d = common difference


tn = nth terms


Hence, by given condition we get,


9 + (n – 1) × ( – 2) = 24 + (n – 1) × ( – 3)


9 – 2n + 2 = 24 – 3n + 3


11 – 2n = 27 – 3n


3n – 2n = 27 – 11


n = 16


Thus, value of nth term where a = 9, d = – 2, n = 16 is


tn = 9 + (16 – 1) × ( – 2)


tn = 9 – 15 × 2


tn = 9 – 30 = – 21


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