The sum of the squares of two natural consecutive odd numbers is

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Which one of the numbers is divisible by 25?

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28.

The odd term in the sequence
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29.

The sum of the squares of two natural consecutive odd numbers is 394. The sum of the numbers is

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D.

40

Let x and x+2 be the two consecutive odd numbers.
rightwards double arrow space space space straight x squared plus space left parenthesis straight x plus 2 right parenthesis squared space equals space 394
rightwards double arrow space space straight x squared plus straight x squared plus 4 plus 4 straight x space equals space 394
rightwards double arrow space space 2 straight x squared plus 4 straight x minus 390 space equals space 0
rightwards double arrow space straight x squared plus 2 straight x minus 195 space equals space 0

rightwards double arrow space straight x squared plus 15 straight x minus 13 straight x minus 195 space equals space 0
rightwards double arrow space space straight x left parenthesis straight x plus 15 right parenthesis space minus 13 left parenthesis straight x plus 15 right parenthesis space equals space 0
rightwards double arrow space left parenthesis straight x minus 13 right parenthesis thin space left parenthesis straight x plus 15 right parenthesis space equals space 0
rightwards double arrow space space straight x space equals space 13 space comma space minus 15
rightwards double arrow space straight x space equals space 13
So, the numbers are (x = 13), (x+2 = 13+2 = 15)
∴  The required sum = 13 + 15 = 28

Shortcut Method:
By mental operation,
   132 + 152 = 169 + 225  = 394
∴  The required sum = 13 + 15 = 28
   



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30.

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