# Maths

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in sequence 4,7,10,13....
PROVE the difference between squared of any two terms is a multiple of 3

• Maths -

since Tn = 1+3n
(Tn)^2 = 1+6n+9n^2
(Tk)^2 = 1+6k+9k^2

(Tn)^2 - (Tk)^2 = (1+6n+9n^2) - (1+6k+9k^2)
= 6n-6k + 9n^2-9k^2
= 3(2n-2k + 3n^2-3k^2)
which is a multiple of 3 for any k,n

• Maths -

thanks - very much.

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