Class 6 - Mathematics
Chapter - Algebraic Expressions : Exercise 12.4
Top Block 1
Question : 1.Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.
(a) 
……..
11 16 21… (5n+1)…
(b) 
……..
7 10 13… (3n+1)…
(c) 
……..
7 121722…
If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern.
How many segments are required to form 5, 10, 100 digits of the kind
Answer :
| SNo. | Symbol | Digit’s Number | Pattern’s Formulae | No. of Segments |
|---|---|---|---|---|
| (i) |  | 5 | 5n + 1 | 26 |
| 10 | 51 | |||
| 100 | 501 | |||
| (ii) |  | 5 | 3n + 1 | 16 |
| 10 | 31 | |||
| 15 | 301 | |||
| (iii) |  | 5 | 5n + 2 | 27 |
| 10 | 52 | |||
| 15 | 502 |
(i) 5n+1
Putting n=5, 5 x 5 + 1 = 25 + 1 = 26
Putting n=10, 5 x 10 + 1 = 50 + 1 = 51
Putting n=100, 5 x 100 + 1 = 500 + 1 = 501
(ii) 3n+1
Putting n=5, 3 x 5 + 1 = 15 + 1 = 16
Putting n=10, 3 x 10 + 1 = 30 + 1 = 31
Putting n=100, 3 x 100 + 1 = 300 + 1 = 301
(iii) 5n+2
Putting n=5, 5 x 5 + 2 = 25 + 2 = 27
Putting n=10, 5 x 10 + 2 = 50 + 2 = 52
Putting n=100, 5 x 100 + 2 = 500 + 2 = 502
Mddle block 1
Question : 2.Use the given algebraic expression to complete the table of number patterns:
| S.No. | Expression | Terms | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1st | 2nd | 3rd | 4th | 5th | ….. | 10th | ….. | 100th | …. | ||
| (i) | 2n – 1 | 1 | 3 | 5 | 7 | 9 | — | 19 | — | — | — |
| (ii) | 3n + 2 | 2 | 5 | 8 | 11 | — | — | — | — | — | — |
| (iii) | 4n + 1 | 5 | 9 | 13 | 17 | — | — | — | — | — | — |
| (iv) | 7n + 20 | 27 | 34 | 41 | 48 | — | — | — | — | — | — |
| (v) | n2 + 1 | 2 | 5 | 10 | 17 | — | — | — | — | 10001 | — |
Answer :
(i) 2n–1
Putting n=100, 2 x 100 – 1 = 200 – 1 = 199
(ii) 3n+2
Putting n=5, 3 x 5 + 2 = 15 + 2 = 17
Putting n=10, 3 x 10 + 2 = 30 + 2 = 32
Putting n=100, 3 x 100 + 2 = 300 + 2 = 302
(iii) 4n+1
Putting n=5, 4 x 5 + 1 = 20 + 1 = 21
Putting n=10, 4 x 10 + 1 = 40 + 1 = 41
Putting n=100, 4 x 100 + 1 = 400 + 1 = 401
(iv) 7n+20
Putting n=5, 7 x 5 + 20 = 25 + 20 = 55
Putting n=10, 7 x 10 + 20 = 70 + 20 = 90
Putting n=100, 7 x 100 + 20 = 700 + 20 = 720
(v) n2+1
Putting n=5, 5 x 5 + 1 = 25 + 1 = 26
Putting n=10, 10 x 10 + 1 = 100 + 1 = 101
Putting n=100, 100 x 100 + 1 = 10000 + 1 = 10001
Now complete table is,
| S.No. | Expression | Terms | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1st | 2nd | 3rd | 4th | 5th | ….. | 10th | ….. | 100th | …. | ||
| (i) | 2n – 1 | 1 | 3 | 5 | 7 | 9 | — | 19 | — | 199 | — |
| (ii) | 3n + 2 | 2 | 5 | 8 | 11 | 17 | — | 32 | — | 302 | — |
| (iii) | 4n + 1 | 5 | 9 | 13 | 17 | 21 | — | 41 | — | 401 | — |
| (iv) | 7n + 20 | 27 | 34 | 41 | 48 | 55 | — | 90 | — | 720 | — |
| (v) | n2 + 1 | 2 | 5 | 10 | 17 | 26 | — | 101 | — | 10001 | — |