91Ó°ÊÓ

In Exercises 33-40, write a rule for the \(n\)th term of the geometric sequence. $$ a_2=-72, a_6=-\frac{1}{18} $$

Your salary is given by the explicit rule \(a_n=35,000(1.04)^{n-1}\), where \(n\) is the number of years you have worked. Write a recursive rule for your salary.

Write an explicit rule for the sequence. $$ a_1=13, a_n=4 a_{n-1} $$

Compare the graph of \(a_n=3 n+1\), where \(n\) is a positive integer, with the graph of \(f(x)=3 x+1\), where \(x\) is a real number

Describe how doubling each term in an arithmetic sequence changes the common difference of the sequence. Justify your answer.

Write an explicit rule for the sequence. $$ a_1=-5, a_n=\frac{1}{4} a_{n-1} $$

A grocery store arranges cans in a pyramid-shaped display with 20 cans in the bottom row and two fewer cans in each subsequent row going up. The number of cans in each row is represented by the recursive rule \(a_1=20\), \(a_n=a_{n-1}-2\). Write an explicit rule for the number of cans in row \(n\).

The value of a car is given by the recursive rule \(a_1=25,600, a_n=0.86 a_{n-1}\), where \(n\) is the number of years since the car was new. Write an explicit rule for the value of the car after \(n\) years.

fi nd the sum. \(\sum_{i=1}^{41}(-2.3+0.1 i)\)

What is the 873rd term of the sequence whose first term is \(a_1=0.01\) and whose \(n\)th term is \(a_n=1.01 a_{n-1}\) ? Justify your answer. (A) \(58.65\) (B) \(8.73\) (C) \(1.08\) (D) \(586,459.38\)