Let S
n =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.
| Sn = |
n |
[2a + (n - 1)d] |
= |
45 |
x [2 x 1 + (45 - 1) x 1] |
= |
❨ |
45 |
x 46 |
❩ |
= (45 x 23) |
| 2 |
2 |
2 |
= 45 x (20 + 3)
= 45 x 20 + 45 x 3
= 900 + 135
= 1035.
Shorcut Method:
| Sn = |
n(n + 1) |
= |
45(45 + 1) |
= 1035. |
| 2 |
2 |
