Question

What will come in place of question mark (?) in the following question?

(625 × 5^{n + 1} – 25 × 5ⁿ)/(25 × 5^{n + 2} – 5 × 5^{n + 2}) = ?

1. 6.2
2. 6
3. 5.8
4. 6.4

Answer 1

Correct Answer - Option 1 : 6.2

Given:

(625 × 5^{n + 1} – 25 × 5ⁿ)/(25 × 5^{n + 2} – 5 × 5^{n + 2}) = ?

Concept used:

(a^{n + 2} + aⁿ) = aⁿ(a² + 1)

Calculation:

(625 × 5^{n +1} – 25 × 5ⁿ)/(25 × 5^{n + 2} – 5 × 5^{n + 2}) = ?

Take common 5ⁿ numerator and denomineator 

⇒ 5ⁿ (625 × 5 – 25)/5ⁿ (25 × 5² – 5 × 5²) = ?

⇒ (3125 – 25)/(25 × 25 - 5 × 25 ) = ?

⇒ 3100/(625 - 125) = ?

⇒ 3100/500 = ?

⇒ 31/5 = ?

⇒ 6.2 = ?

∴ The value of ‘?’ is 6.2.