Observe the following pattern and extend it to three steps- 6 times 2 - 5 -7 7 times 3 - 12 -9 8 times 4 - 21 -11 9 times 5 - 32 -13 - times - - - - - times - - - - - times - - - - -

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Standard VI

Maths

Patterns in Numbers

Question

Observe the following pattern and extend it to three more steps:
$$6 \times 2 - 5 =7 $$
$$7 \times 3 - 12 =9 $$
$$8 \times 4 - 21 =11 $$
$$ 9 \times 5 - 32 =13 $$
$$... \times ... - ... = ...$$
$$... \times ... - ... = ...$$
$$... \times ... - ... = ...$$

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Solution

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Similar Questions

Observe the following pattern and extend it to three more steps:

6 × 2 − 5 = 7
7 × 3 − 12 = 9
8 × 4 − 21 = 11
9 × 5 − 32 = 13
.... × .... − ..... = ......
.... × .... − ..... = ......
.... × .... − ..... = ......

View Solution

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

View Solution

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

View Solution

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) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

View Solution

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 =______=________

View Solution

Observe the following pattern and extend it to three more steps: $$6 \times 2 - 5 =7 $$$$7 \times 3 - 12 =9 $$$$8 \times 4 - 21 =11 $$$$ 9 \times 5 - 32 =13 $$$$... \times ... - ... = ...$$$$... \times ... - ... = ...$$$$... \times ... - ... = ...$$

Observe the following pattern and extend it to three more steps:
$$6 \times 2 - 5 =7 $$
$$7 \times 3 - 12 =9 $$
$$8 \times 4 - 21 =11 $$
$$ 9 \times 5 - 32 =13 $$
$$... \times ... - ... = ...$$
$$... \times ... - ... = ...$$
$$... \times ... - ... = ...$$