9. Sequences, Series, & Induction

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. a+ar+ar²+⋯+ ar¹²

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. $a+(a+d)+(a+2d)+\cdots +(a+nd)$

In Exercises 61–68, use the graphs of and to find each indicated sum.

${\sum }_{i=1}^5(a_i^2+1)$

In Exercises 61–68, use the graphs of and to find each indicated sum.

${\sum }_{i=1}^5(2a_i+b_i)$

In Exercises 61–68, use the graphs of and to find each indicated sum.

${\sum }_{i=1}^5(a_i+3b_i)$

In Exercises 61–68, use the graphs of and to find each indicated sum.

${\sum }_{i=4}^5(a_i/b_i{)}^2$

In Exercises 61–68, use the graphs of and to find each indicated sum.

${\sum }_{i=4}^5(a_i/b_i{)}^3$

In Exercises 61–68, use the graphs of and to find each indicated sum.

${\sum }_{i=1}^5{a}_i^2+{\sum }_{i=1}^5{b}_i^2$

In Exercises 61–68, use the graphs of and to find each indicated sum.

${\sum }_{i=1}^5{a}_i^2-{\sum }_{i=3}^5{b}_i^2$

In Exercises 81–85, use a calculator's factorial key to evaluate each expression.

$\frac{200!}{198!}$

In Exercises 81–85, use a calculator's factorial key to evaluate each expression.

$\frac{20!}{300}$

In Exercises 81–85, use a calculator's factorial key to evaluate each expression.

$\frac{54!}{(54-3)!3!}$

Write the first five terms of the sequence whose first term is 9 and whose general term is

for n≥2.