The arithmetic series is given as ,
[tex]5\text{ + 9 + 13 + 17 + }\ldots\ldots+\text{ 49 }[/tex]From the given sequence ,
[tex]\begin{gathered} a\text{ = 5} \\ d\text{ = 9 - 5 = 4} \end{gathered}[/tex]nth term of the arithmetic series is given as,
[tex]\begin{gathered} a_n\text{ = a + (n-1)d} \\ 49_{}\text{ = 5 + (n-1) 4} \\ 49\text{ = 5 + 4n - 4} \end{gathered}[/tex]Further ,
[tex]\begin{gathered} 49\text{ = 1 + 4n} \\ 4n\text{ = 48} \\ n\text{ = }\frac{48}{4} \\ n\text{ = 12} \end{gathered}[/tex]Sum of the arithmetic series is calculated as,
[tex]\begin{gathered} \text{Sum = }\frac{n}{2}\text{ ( a + l )} \\ \text{Sum = }\frac{12}{2}\text{ ( 5 + 49 )} \\ \text{Sum = 6 }\times\text{ 54} \\ \text{Sum = 324} \end{gathered}[/tex]Thus the sum of the given sequence is 324 .
