Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: From Patterns to Generalizations: Sequences and Series, Exercise 23: Exercise 1G

For a geometric sequence has $r=-\frac{4}{5} \text{and} u_6=-1280$, find the ${20}^{\mathrm{th}}$ term.

If $16,x+2,1$ are the first three terms of a geometric sequence, find all possible values of $x$.

Find the number of terms in the geometric sequence $6,12,24,\dots ,1536$.

Find the possible values of the common ratio of a geometric sequence whose first term is $2$ and whose fifth term is $32$ .

In $2017$, the number of students enrolled in a high school was $232$ It is estimated that the student population will increase by $3\%$ every year. Estimate the number of students that will be enrolled in $2027$.

An old legend states that a peasant won a reward from a king. The peasant asked to be paid in rice; one grain on the first square of a chessboard, two grains on the second, four on the third square, and so on. How many grains of rice would be on the ${30}^{\mathrm{th}}$ square?

An old legend states that a peasant won a reward from a king. The peasant asked to be paid in rice; one grain on the first square of a chessboard, two grains on the second, four on the third square, and so on. Which square would contain exactly $512$ grains of rice?

Given $u_1=8\text{ and }{u}_5=128$, find the values of $u_2,u_3\text{ and }{u}_4$ such that the sequence is geometric.