Math logic and reasoning

1. Tyson was working with square numbers. He noticed a pattern for squaring consecutive
numbers that end in 5

note:top column has 5^2,15^2,25^2,35^2

note: Bottom column shows answers of top column so 5^2=25,15^2=225,25^2=625,
35^2=1225

A.) Identify a pattern in the table.

B.)Make a conjecture based on the pattern identified.

C.) Test the conjecture.

D.) Explain whether or not the conjecture will always work.

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  1. so, see any pattern there?

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  2. Yes sir I see the pattern, just need help with the conjecture part question (B) to (D)

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  3. so, what is the pattern you see?
    The conjecture will be to connect that pattern with the idea of
    "pattern for squaring consecutive numbers that end in 5"

    for D, consider the square of of one of these numbers: 10k+5
    (10k+5)^2 = 100k^2 + 100k + 25

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  4. well we can identify each top nukber goes up by 10 each time, furthermore bottom number all end in 25,

    but for question C how do I show in order to test the conjecture

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  5. well, just square some other numbers ending in 5!

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  6. Your answer should be C

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