Why this series occurs in square numbers-1 imes 1-1- - 2 imes 2-4 - difference -32 times 2-4- - 3 3-9 - difference -5 13 3-9- - 4 4-16 - difference -7 4 imes 4-16- - 5 times 5-25 - difference -96 imes 6-36- - 7 7-49 - difference -13 17 7-49- - 8 8-64 - difference -15

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Quantitative Aptitude

Divisibility Rule for Composite Numbers

Why this seri...

Question

Why this series occurs in square numbers.
$0 \times 0 = 0, 1 \times 1 = 1 d i f f e r e n c e = 1 1 \times 1 = 1, 2 \times 2 = 4 d i f f e r e n c e = 3 2 \times 2 = 4, 3 \times 3 = 9 d i f f e r e n c e = 5 3 \times 3 = 9, 4 \times 4 = 16 d i f f e r e n c e = 7 4 \times 4 = 16, 5 \times 5 = 25 d i f f e r e n c e = 9 5 \times 5 = 25, 6 \times 6 = 36 d i f f e r e n c e = 11 6 \times 6 = 36, 7 \times 7 = 49 d i f f e r e n c e = 13 7 \times 7 = 49, 8 \times 8 = 64 d i f f e r e n c e = 15$

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Solution

There is theorem between this theory.
The difference of square of two consecutive integer is an odd integer.

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Similar questions

$(- 2) \times (- 2) \times 2 \times - 2 = - 16$

Question 5

Study the pattern:
$\begin{matrix} 1 \times 8 + 1 = 9; & 12 \times 8 + 2 = 98; & 123 \times 8 + 3 = 987 1234 \times 8 + 4 = 9876; & 12345 \times 8 + 5 = 98765 \end{matrix}$

Write the next two steps. Can you say how the pattern works?

7 \times 8 - 8 \times 4

Q. Find the value of :

(i) \frac{6.25 \times 6.25 - 1.75 \times 1.75}{4.5} (i i) \frac{198 \times 198 - 102 \times 102}{96}

Choose the correct answers from the given options .

8 \times (3 + 2 \times 2) = ?

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Why this series occurs in square numbers. 0×0=0, 1×1=1 difference=11×1=1, 2×2=4 difference=32×2=4, 3×3=9 difference=53×3=9, 4×4=16 difference=74×4=16, 5×5=25 difference=95×5=25, 6×6=36 difference=116×6=36, 7×7=49 difference=137×7=49, 8×8=64 difference=15

There is theorem between this theory. The difference of square of two consecutive integer is an odd integer.

There is theorem between this theory.
The difference of square of two consecutive integer is an odd integer.