Question

Use summation notation to write the series for five terms

Answer 1

`\large\boxed{\sum\limits_(n=1)^5(-2.2+8.8n)}`

Explanation:

`6.6,\ 15.4,\ 24.2,\ ...\\\\\text{It's an arithmetic sequence:}\\\\15.4-6.6=8.8\\24.2-15.4=8.8\\\\\text{The difference is constant.}\\\\\text{The explicit formula of an arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\\text{Substitute:}\\\\a_1=6.6\ \text{and}\ d=8.8\\\\a_n=6.6+(n-1)(8.8)=6.6+8.8n-8.8=8.8n-2.2\\\\\text{Therefore}\\\\\sum\limits_(n=1)^5(8.8n-2.2)`