If 52- 54- 56- - - - 52 n-0-04-28 what is n -

The given equation is ⇒ 5(2 + 4 + 6 + … + 2n) = (0.04)−28 … (1) 2 + 4 + 6 + … + 2n = 2(1 + 2 + 3 + … + n) From (1) and (2), we get: ⇒ n2 + n − 56 = 0 ...

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Byju's Answer

Standard VII

Mathematics

Forming Equation from Solution

If 52× 54× 56...

Question

If 5² × 5⁴ × 5⁶ × ……× 5²ⁿ = (0.04)⁻²⁸ what is n?

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Solution

The given equation is

⇒ 5^{(2 + 4 + 6 + … + 2n)} = (0.04)⁻²⁸ … (1)

2 + 4 + 6 + … + 2n

= 2(1 + 2 + 3 + … + n)

From (1) and (2), we get:

⇒ n² + n − 56 = 0

⇒ n² + 8n − 7n − 56 = 0

⇒ n(n + 8) − 7(n + 8) = 0

⇒ (n + 8)(n − 7) = 0

⇒ n = −8 or 7

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Similar questions

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What should be subtracted from

\frac{- 5}{3} to get \frac{5}{6} ?

(a)

\frac{5}{2}

(b)

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Q. Solve:

\frac{2}{5} + \frac{3}{5^{2}} + \frac{2}{5^{3}} + \frac{3}{5^{4}} + \frac{2}{5^{5}} + \frac{3}{5^{6}} + . . . . . .

Q. What is the sum of the series

(\frac{1}{5} + \frac{2}{5^{2}} + \frac{3}{5^{3}}) + (\frac{1}{5^{4}} + \frac{2}{5^{5}} + \frac{3}{5^{6}}) + . . . . . . . .

7

terms?

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If 52 × 54 × 56 × ……× 52n = (0.04)−28 what is n?

The given equation is ⇒ 5(2 + 4 + 6 + … + 2n) = (0.04)−28 … (1) 2 + 4 + 6 + … + 2n = 2(1 + 2 + 3 + … + n) From (1) and (2), we get: ⇒ n2 + n − 56 = 0 ⇒ n2 + 8n − 7n − 56 = 0 ⇒ n(n + 8) − 7(n + 8) = 0 ⇒ (n + 8)(n − 7) = 0 ⇒ n = −8 or 7

If 5² × 5⁴ × 5⁶ × ……× 5²ⁿ = (0.04)⁻²⁸ what is n?

The given equation is

⇒ 5^{(2 + 4 + 6 + … + 2n)} = (0.04)⁻²⁸ … (1)

2 + 4 + 6 + … + 2n

= 2(1 + 2 + 3 + … + n)

From (1) and (2), we get:

⇒ n² + n − 56 = 0

⇒ n² + 8n − 7n − 56 = 0

⇒ n(n + 8) − 7(n + 8) = 0

⇒ (n + 8)(n − 7) = 0

⇒ n = −8 or 7