The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of the first 2n terms of another AP whose first term is – 30 and the common difference is 8. The value of n is

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answer is B.

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Detailed Solution

Given,

Also given,
For the series 1, a=8, and d=20.
For the series 2, a'=-30, and d'=8.
Putting these values,

n 2 2 a + n − 1 d for S n and 2 n 2 2 a ′ + 2 n − 1 d ′ for S 2 n in S n = S 2 n

. Substitute 8 for a and 20 for d and -30 for a' and 8 for d' in

2 a + n − 1 d = 2 2 a' + 2 n − 1 d'

to obtain the number of terms.
So,

2 a + n − 1 d = 2 2 a + 2 n − 1 d 28 + n − 1 20 = 2 2 − 30 + 2 n − 1 8 16 + 20 n − 20 = 2 − 60 + 16 n − 8 20 n − 4 = 2 16 n − 68

20 n − 4 = 32 n − 136 32 n − 20 n = − 4 + 136 12 n = 132

n = 13212 n = 11

Thus, the number of terms will be 11.
Therefore, the correct option is 2.

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