Question

Three geometric means between 5 and 3125 are___.

• A. 15,75,375
• B. 25,125,625
• C. 11,44,176
• D. 10,40,160

Answer 1

The correct option is B 25,125,625

The geometric mean is a geometric series which is in the form of arⁿ where a is the first term and r is the common ratio.

T₁= 5 and T₅ = 3125

Now, T₁/T₅ = 5/ 3125

=>ar^1//ar⁵ =1/ 625

=> 1/ r⁴ = 1/625

=> r⁴ = 625

=> r = 5

So if r=5, then a= 1

T₂ = ar²

= 1(5) ² = 25

T₃ = ar³

= 1(5) ³ = 125

T₄ = ar⁴

= 1(5)⁴ = 625

Therefore, three geometric means between 5 and 3125 are 25, 125 and 625.