Chapter 12 Algebraic Expressions Exercise 12.4
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 | 5 | 8 | 11 | 14 | – | – | – | – | – | – |
(iii) | 4n + 1 | 5 | 9 | 13 | 17 | – | – | – | – | – | – |
(iv) | 7n + 20 | 27 | 34 | 41 | 48 | – | – | – | – | – | – |
(v) | n2 + 1 | 2 | 5 | 10 | 17 | – | – | – | – | 10,001 | – |
Solution:
(i) Given expression is 2n – 1
For n = 100, 2 × 100 – 1
= 200 – 1 = 199
(ii) Given expression is 3n + 2
For n = 5, 3 × 5 + 2 = 15 + 2 = 17
For n = 10, 3 × 10 + 2 = 30 + 2 = 32
For n = 100, 3 × 100 + 2 = 300 + 2 = 302
(iii) Given expression is 4n + 1
For n = 5, 4 × 5 + 1 = 20 + 1 = 21
For n = 10, 4 × 10 + 1 = 40 + 1 = 41
For n = 100, 4 × 100 + 1 = 400 + 1 = 401
(iv) Given expression is 7n + 20
For n = 5, 7 × 5 + 20 = 35 + 20 = 55
For n = 10, 7 × 10 + 20 = 70 + 20 = 90
For n = 100, 7 × 100 + 20 = 700 + 20 = 720
(v) Given expression is n2 + 1
For n = 5, 52 + 1 = 25 + 1 = 26
For n = 10, 102 + 1 = 100 + 1 = 101
