Question

If the sum of the first n terms of the series √3 + √75 + √243 + √507 + ..... is 435√3, then n equals

(A)   29

(B)  18

(C) 15

(D)  13

Answer 1

Correct option  (c)  15

 Rewriting the given equation, we get

The given series is AP where a = √3 and d = 4√5

Now, the sum of AP is expressed as

Sn = n/2[]2a + [2a + (n - 1)d]

It is given that Sn = 435√3. Therefore, 

n/2[2a + (n - 1)d] = 435√3

Substituting the values of a and d, we get

 

It is obvious that n = -29/2 cannot be correct value and hence the correct value is n = 15.