If 5 2 5 4 5 6 … . 5 2 n = 0.04 - 28 , then the value of n is equal to

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Question: Answered & Verified by Expert

If

{(5)}^{2} {(5)}^{4} {(5)}^{6} \dots . {(5)}^{2 n} = {(0.04)}^{- 28}

, then the value of

n

is equal to

MathematicsSequences and SeriesJEE Main

Options:

A $7$
B $5$
C $6$
D $3$

Solution:

2280 Upvotes Verified Answer

The correct answer is:

7

The given equation can be written as

5^{2} {(5^{2})}^{2} {(5^{2})}^{3} \dots {(5^{2})}^{n} = {(5^{2})}^{28}

{(5^{2})}^{1 + 2 + 3 + \dots + n} = {(5^{2})}^{28}

\Rightarrow \frac{n (n + 1)}{2} = 28

\Rightarrow n = 7

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