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
.... × .... − ..... = ......
.... × .... − ..... = ......
.... × .... − ..... = ......

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Solution

6 × 2 − 5 = 7
7 × 3 − 12 = 9
8 × 4 − 21 = 11
9 × 5 − 32 = 13
10 × 6 − 45 = 15
11 × 7 − 60 = 17
12 × 8 − 77 = 19

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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. Observe the following pattern and find the next step.

1 \times 8 + 1 = 9

12 \times 8 + 2 = 98

123 \times 8 + 3 = 987

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

Q. Find the values of the following using formulae.

(1) 52²
(2) 98²
(3) 63²
(4) 32 × 28
(5) 77 × 83

Q. Observe the following pattern
2² − 1² = 2 + 1
3² − 2² = 3 + 2
4² − 3² = 4 + 3
5² − 4² = 5 + 4
and find the value of
(i) 100² − 99²
(ii) 111² − 109²
(iii) 99² − 96²

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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 .... × .... − ..... = ...... .... × .... − ..... = ...... .... × .... − ..... = ......

6 × 2 − 5 = 7 7 × 3 − 12 = 9 8 × 4 − 21 = 11 9 × 5 − 32 = 13 10 × 6 − 45 = 15 11 × 7 − 60 = 17 12 × 8 − 77 = 19

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
.... × .... − ..... = ......
.... × .... − ..... = ......
.... × .... − ..... = ......

6 × 2 − 5 = 7
7 × 3 − 12 = 9
8 × 4 − 21 = 11
9 × 5 − 32 = 13
10 × 6 − 45 = 15
11 × 7 − 60 = 17
12 × 8 − 77 = 19