91Ó°ÊÓ

State whether the sequence is arithmetic or geometric. $$0.9,0.81,0.729, \ldots$$

Determine whether the infinite geometric series has a sum. If so, find the sum. $$6+3+\frac{3}{2}+\frac{3}{4}+\cdots$$

State whether the sequence is arithmetic or geometric. $$0.4,0.8,1.6,3.2, \dots$$

Determine whether the infinite geometric series has a sum. If so, find the sum. $$8+4+2+1+\cdots$$

State whether the sequence is arithmetic or geometric. $$0.4,0.9,1.4,1.9, \ldots$$

In this set of exercises, you will use sequences to study real-world problems. Investment An income-producing investment valued at \(\$ 2000\) pays interest at an annual rate of \(6 \% .\) Assume that the interest is taken out as income and therefore is not compounded. (a) Make a table in which you list the initial investment along with the total value of the investment-related assets (initial investment plus total interest earned) at the end of each of the first 4 years. (b) What is the total value of the investment-related assets after \(n\) years?

Determine whether the infinite geometric series has a sum. If so, find the sum. $$9+3+1+\frac{1}{3}+\frac{1}{9}+\cdots$$

In this set of exercises, you will use sequences to study real-world problems. Investment An income-producing investment valued at \(\$ 3000\) pays interest at an annual rate of \(4.5 \% .\) Assume that the interest is taken out as income and therefore is not compounded. (a) Make a table in which you list the initial investment along with the total value of the investment-related assets (initial investment plus total interest earned) at the end of each of the first 4 years. (b) What is the total value of the investment-related assets after \(n\) years?

Determine whether the infinite geometric series has a sum. If so, find the sum. $$12+3+\frac{3}{4}+\frac{3}{12}+\cdots$$

Determine whether the infinite geometric series has a sum. If so, find the sum. $$4+8+16+32+\cdots$$