Chapter 15

In your own words, explain how to construct Pascal’s triangle.

What is the difference between an arithmetic and a geometric series?

Write out the first five terms of each sequence. $$a_{n}=n+2$$

What is an arithmetic sequence? Give an example.

What are the first and last terms in the expansion of \((a+b)^{n} ?\)

Write out the first five terms of each sequence. $$a_{n}=n-4$$

How do you find the common difference for an arithmetic sequence?

Use Pascal’s Triangle to expand each binomial. $$(r+s)^{3}$$

Find the common ratio, \(r,\) for each geometric sequence. $$1,2,4,8, \dots$$

Write out the first five terms of each sequence. $$a_{n}=3 n-4$$

Determine whether each sequence is arithmetic. If it is, find the common difference, \(d\). $$3,11,19,27,35, \dots$$

Use Pascal’s Triangle to expand each binomial. $$(m+n)^{4}$$

Find the common ratio, \(r,\) for each geometric sequence. $$3,12,48,192, \dots$$

Write out the first five terms of each sequence. $$a_{n}=4 n+1$$

Determine whether each sequence is arithmetic. If it is, find the common difference, \(d\). $$4,7,10,13,16, \dots$$

Use Pascal’s Triangle to expand each binomial. $$(y+z)^{5}$$

Find the common ratio, \(r,\) for each geometric sequence. $$9,3,1, \frac{1}{3}, \dots$$

Write out the first five terms of each sequence. $$a_{n}=2 n^{2}-1$$

Determine whether each sequence is arithmetic. If it is, find the common difference, \(d\). $$10,6,2,-2,-6, \dots$$

Use Pascal’s Triangle to expand each binomial. $$(c+d)^{6}$$

Find the common ratio, \(r,\) for each geometric sequence. $$8,4,2,1, \dots$$

Write out the first five terms of each sequence. $$a_{n}=2 n^{2}+3$$

Determine whether each sequence is arithmetic. If it is, find the common difference, \(d\). $$27,20,13,6,-1, \dots$$

Use Pascal’s Triangle to expand each binomial. $$(x+5)^{4}$$

Find the common ratio, \(r,\) for each geometric sequence. $$-2, \frac{1}{2},-\frac{1}{8}, \frac{1}{32}, \dots$$

Write out the first five terms of each sequence. $$a_{n}=3^{n-1}$$

Use Pascal’s Triangle to expand each binomial. $$(k+2)^{5}$$

Find the common ratio, \(r,\) for each geometric sequence. $$2,-6,18,-54, \dots$$

Write out the first five terms of each sequence. $$a_{n}=2^{n}$$

In your own words, explain how to evaluate \(n !\) for any positive integer.

Write the first five terms of the geometric sequence with the given first term and common ratio. $$a_{1}=2, r=5$$

Write out the first five terms of each sequence. $$a_{n}=5 \cdot\left(\frac{1}{2}\right)^{n}$$

Determine whether each sequence is arithmetic. If it is, find the common difference, \(d\). $$-17,-14,-11,-8,-5, \dots$$

Evaluate \(0 !\)

Write out the first five terms of each sequence. $$a_{n}=6 \cdot\left(\frac{1}{3}\right)^{n-1}$$

Determine whether each sequence is arithmetic. If it is, find the common difference, \(d\). $$-12,-10,-8,-6,-4, \dots$$

Write out the first five terms of each sequence. $$a_{n}=(-1)^{n+1} \cdot 7 n$$

Write the first five terms of each arithmetic sequence with the given first term and common difference. $$a_{1}=7, d=2$$

Evaluate. $$3 !$$

Write the first five terms of the geometric sequence with the given first term and common ratio. $$a_{1}=250, r=\frac{1}{5}$$

Write out the first five terms of each sequence. $$a_{n}=(-1)^{n} \cdot(n+1)$$

Write the first five terms of each arithmetic sequence with the given first term and common difference. $$a_{1}=20, d=4$$

Evaluate. $$5 !$$

Write the first five terms of the geometric sequence with the given first term and common ratio. $$a_{1}=72, r=\frac{2}{3}$$

Write out the first five terms of each sequence. $$a_{n}=\frac{n-4}{n+3}$$

Write the first five terms of each arithmetic sequence with the given first term and common difference. $$a_{1}=15, d=-8$$

Evaluate. $$6 !$$

Write the first five terms of the geometric sequence with the given first term and common ratio. $$a_{1}=-20, r=-\frac{3}{2}$$

Write out the first five terms of each sequence. $$a_{n}=\frac{n^{2}-1}{n}$$

Write the first five terms of each arithmetic sequence with the given first term and common difference. $$a_{1}=-3, d=-2$$