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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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