To find $ S_{ 26 } $ we use formula

$$ \color{blue}{S_n = \frac{n}{2} \cdot \left(2a_1 + (n-1) \cdot d \right) } $$

In this example we have $ a_1 = 9 ~,~ d = 5 ~,~ n = 26 $. After substituting these values into the above equation, we obtain:

$$ \begin{aligned} S_n &= \frac{n}{2} \cdot \left(2a_1 + (n-1) \cdot d \right) \\[1 em] S_{ 26 } &= \frac{ 26 }{2} \cdot \left( 2 \cdot 9 + ( 26-1) \cdot 5 \right) \\[1 em] S_{ 26 } &= \frac{ 26 }{2} \cdot \left( 18 + 25 \cdot 5 \right) \\[1 em] S_{ 26 } &= \frac{ 26 }{2} \cdot \left( 18 + 125 \right) \\[1 em] S_{ 26 } &= \frac{ 26 }{2} \cdot 143 \\[1 em] S_{ 26 } &= 1859 \end{aligned}$$

The first few terms of this sequence are:

$$ 9, ~~~14, ~~~19, ~~~24, ~~~29 . . . $$

Arithmetic sequences