Question

1+2+3+4+5+6+7+................................+100

Answer 1

1+2+3+4+5+6+7+.....................+100

Here first term , a = 1
Common difference, d = a₂ - a₁
                                 = 2 - 1
                                 =1
Number of terms = 100

Sn = n/2 [ 2a + (n-1)d]
Sn = 50[2 + 99]
Sn = 50 × 101
Sn = 5050

Answer 2

If the difference between each term is by 1 
and the series start from 1 
then you can use this formula        $\frac{n(n+1)}{2 }$         where n is number of terms

so using the formula we get      $\frac{100*101}{2}$
                                               

=  50 x 101 = 5050 ANSWER