Respuesta :
first off, let's find the 1st term's value, and the 30th term's value,
[tex]\bf a1=3(1)+2\implies a1=5\qquad \qquad \quad a30=3(30)+2\implies a30=92\\\\ -------------------------------\\\\ ~~~~~~~\textit{ Sum of an arithmetic sequence}\\\\ S_n=\cfrac{n(a1+an)}{2}~ \begin{cases} n=n^{th}\ term\\ a1=\textit{first term's value}\\ ----------\\ a1=5\\ a30=92\\ n=30 \end{cases} \implies S_{30}=\cfrac{30(5+92)}{2} \\\\\\ S_{30}=15(97)[/tex]
[tex]\bf a1=3(1)+2\implies a1=5\qquad \qquad \quad a30=3(30)+2\implies a30=92\\\\ -------------------------------\\\\ ~~~~~~~\textit{ Sum of an arithmetic sequence}\\\\ S_n=\cfrac{n(a1+an)}{2}~ \begin{cases} n=n^{th}\ term\\ a1=\textit{first term's value}\\ ----------\\ a1=5\\ a30=92\\ n=30 \end{cases} \implies S_{30}=\cfrac{30(5+92)}{2} \\\\\\ S_{30}=15(97)[/tex]
Answer:
[tex]S_{30}[/tex]= 1455.
Step-by-step explanation:
Given : an=3n+2.
To find : find the sum of the first 30 terms of the sequence.
Solution : We have given [tex]a_{n}[/tex] = 3n + 2.
For first term n = 1
[tex]a_{1}[/tex] = 3 (1) +2.
[tex]a_{1}[/tex] = 5
For last term n = 30
[tex]a_{30}[/tex] = 3(30) +2
[tex]a_{30}[/tex] = 90 +2
[tex]a_{30}[/tex] = 92.
Then sum of first 30 terms
[tex]S_{30} =\frac{n(First\ term+last\ term)}{2}[/tex].
[tex]S_{30} =\frac{30(5+92)}{2}[/tex].
[tex]S_{30} =\frac{30(97)}{2}[/tex].
[tex]S_{30}[/tex]= 15 *97.
[tex]S_{30}[/tex]= 1455.
Therefore, [tex]S_{30}[/tex]= 1455.
