# If 1 = 5, 2 = 25, 3 = 125, 4 = 625, then 5 = ? Give reasons.

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A pattern is being established in your numerical series of problems. In the first statement, 1 is the equivalent of 5. In the next, 2 is 25, which is actually 5 times 5. In the third set, you are stating that 3 is equal to 125. This is the result of 5 times 5 times 5 which is 125. In the fourth problem, 4 equals 625.This is due to 5 times 5 times 5 times 5 or 625. Finally, following this logical approach, 5 must be equal to 5 times 5 times 5 times 5 times 5 which is equal to 3125. The exponent of a number says how many times to use the number in a multiplication. This problem illustrates the use of exponents.

**Sources:**

You make a good point. First of all, the notation is bad. `1=5` is something that should probably never be written in math. "`=`" should always represent an equivalence relation, which is symmetric, so one would expect that if somehow `1=5`, then `5=1`.

Also, even without the notation, there are infinitely many sequences that start with the terms 5,25,125,625, so strictly speaking, there is no single answer. The next term could be anything.

However, for little riddles like this, usually we overlook bad notation and also make the assumption that the person asking the question wants the "obvious" answer. In this case, that would either be 3125 or 1. It depends on whether the person asking the question was thinking like the first two posters or like you.

5 = 3125

Reasons,

1 = 5 -----> 5^1 = 5

2 = 25 -----> 5^2 = 5x5 = 25

3 = 125 -----> 5^3 = 5x5x5 = 125

4 = 625 -----> 5^4 = 5x5x5x5 = 625

5 = 3125 -----> 5^5 = 5x5x5x5x5 = 3125

**Why can't 5 = 1 when 1 = 5.**