Question

Find the sum of the following arithmetic series: 5+9+13+17+…+49.

Answer 1

The arithmetic series is given as ,

`5\text{ + 9 + 13 + 17 + }\ldots\ldots+\text{ 49 }`

From the given sequence ,

`\begin{gathered} a\text{ = 5} \\ d\text{ = 9 - 5 = 4} \end{gathered}`

nth term of the arithmetic series is given as,

`\begin{gathered} a_n\text{ = a + (n-1)d} \\ 49_{}\text{ = 5 + (n-1) 4} \\ 49\text{ = 5 + 4n - 4} \end{gathered}`

Further ,

`\begin{gathered} 49\text{ = 1 + 4n} \\ 4n\text{ = 48} \\ n\text{ = }(48)/(4) \\ n\text{ = 12} \end{gathered}`

Sum of the arithmetic series is calculated as,

`\begin{gathered} \text{Sum = }(n)/(2)\text{ ( a + l )} \\ \text{Sum = }(12)/(2)\text{ ( 5 + 49 )} \\ \text{Sum = 6 }*\text{ 54} \\ \text{Sum = 324} \end{gathered}`

Thus the sum of the given sequence is 324 .