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If the nth terms of the two APs: 9, 7, 5, ... and 24, 21, 18, … are the same, the value of n is[[1]].

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Detailed Solution

If the nth terms of the two APs: 9, 7, 5, ... and 24, 21, 18, … are the same, the value of n is 16.
The given series are 9, 7, 5, ... and 24, 21, 18, … .
From the first series,

a = 9

d = 7 − 9 d = − 2

For

a n

, let’s put the values of a and d,

a n = a + (n − 1) d = 9 + (n − 1) (− 2) = 9 − 2 n + 2 = 11 − 2 n

From the second series,

a ′ − 24

d = 21 − 24 d = − 3

For

a n

, let’s put the values of a and d,

a n = 24 + n − 1 − 3 = 24 − 3 n − 1 = 24 − 3 n + 3 = 27 − 3 n

Now, let’s equate both the last terms,

a n = a n 27 − 3 n = 11 − 2 n − 3 n + 2 n = 11 − 27 − n = − 16

n = 16

For the value of

a 16

for the first AP.

a n = a + n − 1 d

a 16 = 9 + 16 − 1 − 2 = 9 − 152 = 9 − 30 = − 21

For the value of

a 16

for the second A.P.

a 16 = 24 + 16 − 1 − 3 = 24 − 153 = 24 − 45 = − 21

Thus, the correct answer is 16.

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