Question

Find the sum of the first 60 terms in the seqeunce below an=5n+10

Answer 1

so the sequence is an = 5n+10 hmmmmm what's the 1st term? a1 = 5(1) + 10, or 15 then, hmmmmm what's the 60th term? a60 = 5(60) + 10, or 310.


`\bf \textit{sum of a finite arithmetic sequence}\\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} n=n^(th)\ term\\ a_1=\textit{first term's value}\\ ----------\\ a_1=15\\ a_(60)=310\\ n=60 \end{cases} \\\\\\ S_(60)=\cfrac{60(15+60)}{2}\implies S_(60)=30(75)`