Question

If 5, x, y, z, 80 are in GP then what is the value of x, y, and z?

1. x = 10, y = 20, z = 30
2. x = 10, y = 20, z = 40
3. x = 20, y = 30, z = 40
4. x = 5, y = 20, z = 30
5. None of these

Answer 1

Correct Answer - Option 2 : x = 10, y = 20, z = 40

Concept:

n^th  term of the G.P. is a_n = arⁿ⁻¹

 

Calculation:

GIven series: 5, x, y, z, 80

We have 1st term, a = 5, and 5th term,a5 = 80

∴ a₅ = 5 (r)^5-1

⇒ 80 = 5r⁴

⇒ r⁴ = 16

⇒ r = 2

∴ x = 5(2)^2-1 = 10

And, y = 5(2)^3-1 = 5 × 4 = 20

Also, z = 5(2)^4-1 = 5 × 8 = 40 

Hence, option (2) is correct.