The sum of all the 11 terms of an AP whose middlemost term is 30, is

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300

420

330

450

answer is C.

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Detailed Solution

Given the middlemost term of the AP is 30.
According to the question, n =11.
As the number of terms is odd number, so the middle term will be

11 + 1 2 th term or 6 th

term.
As the middle term is 30 means,

a 6 = 30

.
Equating, n = 6 and

a 6 = 30

a n = a + n − 1 d

a n = a + n − 1 d a 6 = a + 6 − 1 d 30 = a + 5 d a = 30 − 5 d

Now, the sum of all the 11 terms, where n = 11 and a = 30-5d in,

S n = n 2 2 a + n − 1 d

S 11 = 112 2 30 − 5 d + 11 − 1 d = 112 60 − 10 d + 10 d = 11260

S 11 = 1130 = 330

So, the sum of the first 11 terms whose middlemost term is 30 is 330.
Therefore, the correct option is 3.

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