The number of terms in the following A.P.'s are,

6, 3, 0, -3,…..,–36

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answer is B.

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Detailed Solution

Given A.P. is,
6, 3, 0, — 3,…..,–36
We know the formula of last term is,

l = a 1 + n − 1 d

,
where l is the last term and a is the first term and d is the common difference and n is the total number of terms.
Now, the common difference will be,

d = a 2 − a 1 ⇒ d = 3 − 6 ⇒ d = − 3

Now,
Substitute 6 for a and -3 for d and -36 for

l

l = a + n − 1 d

to obtain the number of terms.

− 36 = 6 + n − 1 − 3 ⇒ − 36 = 6 − 3 n + 3 ⇒ − 45 = − 3 n ⇒ n = 15

The number of terms of the arithmetic progression is 15.
Therefore, option 2 is correct.

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