[tex]\displaystyle{a_n=5n+10[/tex]
means that the value of the n'th term of the sequence is 5n+10
for example, the value of the seventh term is [tex]\displaystyle{a_7=5\cdot 7+10=35+10=45[/tex]
The sum of the first 60 terms can be calculated as follows:
[tex]\displaystyle{ a_1+a_2+a_3+...+a_{60}=[/tex]
[tex]\displaystyle{ (5\cdot1+10)+(5\cdot2+10)+(5\cdot3+10)+...(5\cdot60+10)[/tex]
[tex] =5(1+2+3+...59+60)+10\cdot 60[/tex]
using the Gauss formula for the addition of the first n natural numbers:
[tex]1+2+3+...59+60= \frac{60\cdot(61)}{2}=30\cdot61=1,830 [/tex]
thus we have:
[tex]5(1+2+3+...59+60)+10\cdot 60=5\cdot1,830+600[/tex]
[tex]=9,150+600=9,750[/tex]
Answer: 9,750
