Respuesta :
[tex]S_{46\text{ }}\text{ = 3657}[/tex]
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;
[tex]\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}[/tex]Now, we can apply the formula to get the sum
The formula is given as;
[tex]\begin{gathered} Sn\text{ = }\frac{n}{2}\text{ (a + l)} \\ \\ S_{46}\text{ = }\frac{46}{2}(12\text{ + 147)} \\ \\ S_{46}\text{ = 23(159)} \\ \\ S_{46}\text{ = 23 }\times\text{ 159 = 3657} \\ \text{Where the last term is given as l above} \end{gathered}[/tex]