Question

15.a)Form the pattern of reminders formed when the perfect squares are divided by 6. b) Is there any perfect square term in the arithmetic sequence of nth term 6n+2.​

Answer 1

Answer:

sequence of nth term 6n+2.

Answer 2

Pattern of remainder formed when the perfect squares are divided by 6 is:

0 , 1 , 4 , 3 , 4 , 1

Any perfect square term  will not be of form 6n+2

Without losing generality all numbers can be written in the form

as 6n , 6n+1 , 6n+2, 6n+3 , 6n+4 , 6n+5

Squaring the number

(6n)² = 36n² = 6(6n)²   Divisible by 6 hence remainder = 0

(6n + 1)² = 36n² + 12n + 1 = 6(6n² + 2n) + 1  hence remainder = 1

(6n + 2)² = 36n² + 24n +4 = 6(6n² + 4n) + 4  hence remainder = 4

(6n + 3)² = 36n² + 36n + 9 = 6(6n² + 6n+1) + 3  hence remainder = 3

(6n + 4)² = 36n² + 48n +16 = 6(6n² + 8n + 2) + 4  hence remainder = 4

(6n + 5)² = 36n² +60n + 25 = 6(6n² + 10n+4) + 1  hence remainder = 1

Hence pattern of remainder formed when the perfect squares are divided by 6 is:

0 , 1 , 4 , 3 , 4 , 1

As there is no remainder 2 Hence  any perfect square term  will not be of form 6n+2

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