1) Find the value(s) of \(y\) that makes the sequence geometric: \(y + 2,\ 3y – 1,\ 9y +4, ...\)
2) Find the \(3rd\) and \(5th\) term of a geometric sequence where \({a}_{1}=5\), and \({a}_{7}=\large\frac{78,125}{729}\).
3) Find the sum of the geometric series of the first \(11\) terms, to the nearest hundredth: \(4\large-\frac{16}{7}+\frac{64}{49}-...\)
4) A ping pong ball is dropped from the roof of the school, from \(35\) feet above the ground. After it hits the ground it bounces up to a height of \(28\) feet, then \(22.4\) feet and so on. Assuming, the pattern continues at the same rate,
a) What is the total distance, to the nearest hundredth, the ping pong ball will travel after \(7\) bounces?
b) What is the total distance, to the nearest hundredth, the ping pong ball will bounce before it comes to a stop?
5) Find the infinite sum of each geometric series, if it exists.
a) \(4+3+\large\frac{9}{4}\large+\Large\frac{27}{16}...\)
b) \(a_1=20,\ r=\large\frac{5}{2}\)
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2) Find the \(3rd\) and \(5th\) term of a geometric sequence where \({a}_{1}=5\), and \({a}_{7}=\large\frac{78,125}{729}\).
3) Find the sum of the geometric series of the first \(11\) terms, to the nearest hundredth: \(4\large-\frac{16}{7}+\frac{64}{49}-...\)
4) A ping pong ball is dropped from the roof of the school, from \(35\) feet above the ground. After it hits the ground it bounces up to a height of \(28\) feet, then \(22.4\) feet and so on. Assuming, the pattern continues at the same rate,
a) What is the total distance, to the nearest hundredth, the ping pong ball will travel after \(7\) bounces?
b) What is the total distance, to the nearest hundredth, the ping pong ball will bounce before it comes to a stop?
5) Find the infinite sum of each geometric series, if it exists.
a) \(4+3+\large\frac{9}{4}\large+\Large\frac{27}{16}...\)
b) \(a_1=20,\ r=\large\frac{5}{2}\)
Solution Bank