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How many terms of the A.P. 3, 5, 7, 9, ... must be added to get the sum 120?

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answer is A.

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Detailed Solution

Given the A.P. 3, 5, 7, 9, ...
We know that the formula to calculate the sum of n numbers is given by,

S n = n 2 2 a + n − 1 d

.
Where,
The first term is a.
The common difference is d.
The number of terms are n.
The common difference will be,

d = 5 − 3 ⇒ d = 2

Therefore sum of n terms will be,

120 = n 2 23 + n − 1 2 ⇒ 240 = n 6 + 2 n − 2 ⇒ 240 = n 2 n + 4 ⇒ n 2 + 2 n − 120 = 0

⇒ n 2 + 12 n − 10 n − 120 = 0 ⇒ n n + 12 − 10 n + 12 = 0 ⇒ n + 12 n − 10 = 0

Therefore,

n + 12 = 0 ⇒ n = − 12

And,

n − 10 = 0 ⇒ n = 10

Take the positive value n=10 since number of terms cannot be negative.
Hence the value f n is 10.
Therefore, option 1 is correct.

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