Question

Find the sum of the first 46 terms of the following series to the nearest integer 12,15,18

Answer 1

`S_{46\text{ }}\text{ = 3657}`

Here, we want to find the sum of the first 46 terms of the series

Here, what we have is a series with a first term of 12 and a common difference of 15-12=18-15 = 3

Before we proceed to get the sum of the first 46 terms, we can calculate the last term

The last term is given as;

`\begin{gathered} a_n\text{ = a + (n-1)d} \\ \\ a_(46)\text{ = 12 + (46-1)3} \\ \\ a_(46)\text{ = 12 + 45(3)} \\ \\ a_(46)\text{ = 12 + 135 = 147} \end{gathered}`

Now, we can apply the formula to get the sum

The formula is given as;

`\begin{gathered} Sn\text{ = }(n)/(2)\text{ (a + l)} \\ \\ S_(46)\text{ = }(46)/(2)(12\text{ + 147)} \\ \\ S_(46)\text{ = 23(159)} \\ \\ S_(46)\text{ = 23 }*\text{ 159 = 3657} \\ \text{Where the last term is given as l above} \end{gathered}`