In the following, observe the pattern and fill in the blanks.
I + 3 = 4 = $2^{2}$
1+ 3 + 5 = 9 = $3^{2}$
1+ 3 + 5 +7 = 16 = $4^{2}$
1+ 3 + 5 +7 +9 =___ = _
1+ 3 + 5 +7 +9 + 11+ 13+ 15 ==____

$25 = 5^{2}$

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$64 = 8^{2}$

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Solution

Just follow the pattern, each step gives the square of any one number
$1 + 3 = 4 = 2^{2}$
$1 + 3 + 5 = 3^{2} 1 + 3 + 5 + 7 = 4^{2} 1 + 3 + 5 + 7 + 9 = 25 = 5^{2} 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 = 8^{2}$
Therefore, $25 = 5^{2}, 64 = 8^{2}$ is the correct answer.

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Similar questions

Q. Study the following pattern:

1 + 3 = 2 × 2
1 + 3 + 5 = 3 × 3
1 + 3 + 5 + 7 = 4 × 4
1 + 3 + 5 + 7 + 9 = 5 × 5

By observing the above pattern, find

(i) 1 + 3 + 5 + 7 + 9 + 11
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15
(iii) 21 + 23 + 25 + ........ + 51

Q. Without adding, find the sum
(i)

1 + 3 + 5 + 7 + 9

(ii)

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

(iii)

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Re-arrange suitably and find the sum in each of the following :

(i) $\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2}$

(ii) $\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7}$

(iii) $\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}$

(iv) $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$

(v) $\frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5}$

(vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

Name the property of multiplication illustrated by each of the following statements :

(i) $\frac{- 15}{8} \times \frac{- 12}{7} = \frac{- 12}{7} \times \frac{- 15}{8}$

(ii) $(\frac{- 2}{3} \times \frac{7}{9}) \times \frac{- 9}{5} = \frac{- 2}{3} \times (\frac{7}{9} \times \frac{- 9}{5})$

(iii) $\frac{- 3}{4} \times (\frac{- 3}{4} \times \frac{- 5}{6}) + (\frac{- 3}{4} \times \frac{7}{8})$

(iv) $\frac{- 16}{9} \times 1 = 1 \times \frac{- 16}{9} = \frac{- 16}{9}$

(v) $\frac{- 11}{15} \times \frac{15}{- 11} = \frac{15}{- 11} \times \frac{- 11}{15} = 1$

(vi) $\frac{- 7}{5} \times 0 = 0$

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In the following, observe the pattern and fill in the blanks.I + 3 = 4 = 221+ 3 + 5 = 9 = 321+ 3 + 5 +7 = 16 = 421+ 3 + 5 +7 +9 =_______ = _______1+ 3 + 5 +7 +9 + 11+ 13+ 15 =______=________

Just follow the pattern, each step gives the square of any one number1+3=4=221+3+5=321+3+5+7=421+3+5+7+9=25=521+3+5+7+9+11+13+15=64=82 Therefore,25=52,64=82 is the correct answer.

In the following, observe the pattern and fill in the blanks.
I + 3 = 4 = $2^{2}$
1+ 3 + 5 = 9 = $3^{2}$
1+ 3 + 5 +7 = 16 = $4^{2}$
1+ 3 + 5 +7 +9 =___ = _
1+ 3 + 5 +7 +9 + 11+ 13+ 15 ==____

Just follow the pattern, each step gives the square of any one number
$1 + 3 = 4 = 2^{2}$
$1 + 3 + 5 = 3^{2} 1 + 3 + 5 + 7 = 4^{2} 1 + 3 + 5 + 7 + 9 = 25 = 5^{2} 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 = 8^{2}$
Therefore, $25 = 5^{2}, 64 = 8^{2}$ is the correct answer.