7. Observe the pattern and fill in the blanks.<br />3²+ 4²+ 12² = 13²<br />4²+ 5²+ 20² = 21²<br />6² + 7²+ 42²= 43²<br />5²+ 6²+ 30² <br />= 31²<br />(a) 1²+ 2² + - =<br />(b) 5² + - + 30² =<br />(c) _ + 3²+ 6² =<br />(d) 8² + ------- +------ =73² tell me
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"Let's break the first 2 into two 1…..so the series become 1+sum of square of natural numbers from 1 to 13…….the formula for the sum of square of natural numbers starting with 1 is……..( n(n+1)(2n+1) ) / 6……after this add 1 to get the answer…..where n is the number of terms"
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Answer:
(a) 1²+ 2² + 2²= 3²
(b) 5² + 6²+ 30² =31²
(c) 2²+ 3²+ 6² =7²
(d) 8² + 9² + 72²=73²
Step-by-step explanation:
it is n² + (n+1)² + {n(n+1)}² = {n(n+1)+1}²
3×4 = 12
4×5 = 20
3²+ 4²+ 12² = 13²
4²+ 5²+ 20² = 21²
6² + 7²+ 42²= 43²
5²+ 6²+ 30² = 31²
(a) 1²+ 2² + 2²= 3²
(b) 5² + 6²+ 30² =31²
(c) 2²+ 3²+ 6² =7²
(d) 8² + 9² + 72²=73²
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