Question

5^1*5^3*5^5*...5^2n-1=25^72 find n

Answer 1

thus, n=12.
this question is based on Arithmetic Prograsion

Answer 2

The n value is 12

Given:

5¹ × 5³ × 5⁵ × ... 5²ⁿ⁻¹ = 25⁷²  

To find:

The value of n  

Solution:

Given that 5¹ × 5³ × 5⁵ × ... 5²ⁿ⁻¹ = 25⁷²  

⇒ $5^{(1+3+5..)}$  = $5^{2^{72} }$   [ base are equal powers should be added ]

⇒ $5^{(1+3+5..)}$ = $5^{{144} }$  

⇒ 1 + 3 + 5 .. (2n-1)= 144    [ here 1, 3, 5 ..  area odd number ]

We know that sum of first n odd number = n²

⇒ n²  = 144

⇒ n = 12

Therefore, the value of n = 12

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