91Ó°ÊÓ

CONCEPT EXTENSIONS A. Write the sum \(\sum_{i=1}^{7}\left(i+i^{2}\right)\) without summation notation. B. Write the sum \(\sum_{i=1}^{7} i+\sum_{i=1}^{7} i^{2}\) without summation notation. C. Compare the results of parts a and b. D. Do you think the following is true or false? Explain your answer. $$ \sum_{i=1}^{n}\left(a_{n}+b_{n}\right)=\sum_{i=1}^{n} a_{n}+\sum_{i=1}^{n} b_{n} $$

Describe a situation in everyday life that can be modeled by an infinite geometric series.

Evaluate. $$ 2(2-4)+3(3-4)+4(4-4) $$

Evaluate. $$ 3^{0}+3^{1}+3^{2}+3^{3} $$

Evaluate. $$ \frac{1}{4(1)}+\frac{1}{4(2)}+\frac{1}{4(3)} $$

Evaluate. $$ \frac{8-1}{8+1}+\frac{8-2}{8+2}+\frac{8-3}{8+3} $$

Write the first four terms of the arithmetic or geometric sequence whose first term, \(a_{1},\) and common difference, \(d\), or common ratio, \(r\) are given. $$ a_{1}=\$ 3720, d=-\$ 268.50 $$

Write the first four terms of the arithmetic or geometric sequence whose first term, \(a_{1},\) and common difference, \(d\), or common ratio, \(r\) are given. $$ a_{1}=\$ 11,782.40, r=0.5 $$

Write the first four terms of the arithmetic or geometric sequence whose first term, \(a_{1},\) and common difference, \(d\), or common ratio, \(r\) are given. $$ a_{1}=26.8, r=2.5 $$

Write the first four terms of the arithmetic or geometric sequence whose first term, \(a_{1},\) and common difference, \(d\), or common ratio, \(r\) are given. $$ a_{1}=19.652 ; d=-0.034 $$