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 | - | - | - | - | 10001 | |
(i)Expression = 2n - 1
100th term (i.e. n = 100)
= 2(100) - 1
= 200 - 1
= 199
(ii)Expression = 3n + 2
5th term( i.e. n = 5)
= 3(5) + 2
= 15 + 2
= 17
10th terms(i.e.. n =10)
=3(10) + 2
=30 + 2
= 32
100th term( i.e. n = 100)
=3(100) + 2
= 300 + 2
= 302
(iii)Expression = 4n + 1
5th term( i.e. n = 5)
= 4(5) + 1
= 20 + 1
= 21
10th terms(i.e.. n =10)
=4(10) + 1
=40 + 1
= 41
100th term( i.e. n = 100)
=4(100) + 1
= 400 + 1
= 401
(iv)Expression = 7n + 20
5th term( i.e. n = 5)
= 7(5) + 20
= 35 + 20
= 55
10th terms(i.e.. n =10)
=7(10) + 20
=70 + 20
= 90
100th term( i.e. n = 100)
=7(100) + 20
= 700 + 20
= 720
(ii)Expression = n2 + 1
5th term( i.e. n = 5)
= (5)2 + 1
= 25 + 1
= 26
10th terms(i.e.. n =10)
=(10)2 + 1
=100 + 1
= 101
So the 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 | 5 | 8 | 11 | 14 | 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 | |