Question

Find the sum of the first 60 terms of the sequence below a_n=5n+10

Answer 1

`\displaystyle{a_n=5n+10`

means that the value of the n'th term of the sequence is 5n+10

for example, the value of the seventh term is
`\displaystyle{a_7=5\cdot 7+10=35+10=45`


The sum of the first 60 terms can be calculated as follows:


`\displaystyle{ a_1+a_2+a_3+...+a_(60)=`


`\displaystyle{ (5\cdot1+10)+(5\cdot2+10)+(5\cdot3+10)+...(5\cdot60+10)`


`=5(1+2+3+...59+60)+10\cdot 60`


using the Gauss formula for the addition of the first n natural numbers:


`1+2+3+...59+60= (60\cdot(61))/(2)=30\cdot61=1,830`


thus we have:


`5(1+2+3+...59+60)+10\cdot 60=5\cdot1,830+600`


`=9,150+600=9,750`


Answer: 9,750