Consecutive Number

We can tell that this is an arithmetic sequence from the fact that it is increasing by 1 every time you go up one integer. Therefore, we can use the equation ${ S }_{ n }\quad =\quad \frac { 1 }{ 2 } n({ a }_{ 1 }+{ a }_{ n })$ . a sub 1 = 10, n = 41 (because you are counting inclusively), and a sub n = 50. ${ S }_{ 41 }\quad =\quad \frac { 1 }{ 2 } (41)(10+50)\\ \quad \quad \quad =\quad \frac { 1 }{ 2 } (41)(60)\\ \quad \quad \quad =\quad (30)(41)\\ \quad \quad \quad =\quad \boxed { 1230 }$

The series of numbers form an arithmetic progression with $d=1$ and $n=41$ . The formula for the sum of terms is

$S_n=\dfrac{n}{2}(a_1+a_n)$

$S_{41}=\dfrac{41}{2}(10+51)=\boxed{1230}$