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.