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From the following choices, which term of the AP $21, 18, 15, …$ is -81?

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answer is D.

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Detailed Solution

It is given that 21, 18, 15,…, is in AP.
From the given information, the first term,

a 1 = 21

a 2 = 18

The common difference is,

d = a 2 − a 1

d = 18 − 21

d = − 3

Let -81 be the nth term of an AP, so,

a n = − 81

a n = a + (n − 1) d

Substitute the known values in the above formula,

− 81 = 21 + (n − 1) (− 3)

− 3 (n − 1) = − 102 n − 1 = 34

n = 35

-81 is the 35th term of an AP.
Hence, option 4) is correct.

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