5, 13, 21

This is an arithmetic series with $\displaystyle a_1 = 5$ and $\displaystyle d = 8$ .

$\displaystyle S_n = \frac n2 (a_1 + a_n) = \frac n2 \Bigg[a_1 + \bigg(a_1 + d(n - 1)\bigg)\Bigg]$

$\displaystyle S_{50} = \frac {50}{2} \bigg(5 + 5 + 8(49)\bigg)$

$\displaystyle = 10050$

This is an arithmetic progression with $a_1=5$ , $n=50$ and $d=8$

Solution 1

We can use the formula $S=\dfrac{n}{2}[2a_1+(n-1)d]$

$S=\dfrac{50}{2}[2(5)+(50-1)8]=25(10+392)=$ $\color{#3D99F6}\boxed{\large10050}$ $\color{#D61F06}\large\boxed{answer}$

Solution 2

We can use the formula $S=\dfrac{n}{2}(a_1+a_n)$ . But we need to solve for $a_n$ first. In here, our $a_n$ is $a_{50}$ .

Solving for $a_{50}$ , we have

$a_{50}=a_1+(n-1)d=a_1+(50-1)d=5+49(8)=5+392=397$

Finally,

$S=\dfrac{50}{2}(5+397)=25(402)=$ $\color{#3D99F6}\boxed{\large10050}$ $\color{#D61F06}\large\boxed{answer}$