Question

If x be the first term, y be the nth term and p be the product of n terms of a G.P., then the value of p2 will be

(a) (xy)n−1

(b) (xy)n

(c) (xy)1−n

(d) (xy)n/2

Answer 1

Correct option (b) (xy)n

Explanation:

Solve this for a sample GP. Let us say we take the GP as 2, 6, 18, 54. x, the first term is 2, let n = 3 then the 3rd term y = 18 and the product of 3 terms p = 2 × 6 × 18 = 216 = 63 . The value of p2 = 216 × 216 = 66 .

Putting these values in the options we have:

Option (a) gives us (xy)n − 1 = 362 which is not equal to the value of p2 we have from the options

Option (b) gives us (xy)n = 363 = 66 which is equal to the value of p2 we have from the options.

It can be experimentally verified that the other options yield values of p2 which are different from 66 and hence we can conclude that option (b) is correct.