Arithmetic and Geometric Sequences

Select ALL of the arithmetic sequences below.

• {3, 5, 7, 9, 11,...}

• {4, 1, -2, -5, -8,...}

• {9, 14, 20, 39, 55,...}

• {1, 6, 36, 216, 1296,...}

Select ALL of the geometric sequences below.

• {5, 4, 3, 2, 1, 0,...}

• {-3, -6, -12, -24,...}

• {4, 5, 10, 13, 16,...}

• {4, 12, 36, 108,...}

An arithmetic sequence can be described as:

• take the square root of the previous term to get the next term

• dividing a common difference to each term to get the next term

• adding a common difference to each term to get the next term

• multiply the next term to get the previous term

Which equation shows how to find the common ratio, r, for a geometric sequence?

• $a_n-a_{n-1}=r$

• $\frac{a_n}{a_{n-1}}=r$

• $a_n\cdot a_{n-1}=r$

Which equation shows how to find the common difference, d, for an arithmetic sequence?

• $2\cdot a_n=d$

• $\frac{a_{n-1}}{a_n}=d$

• $a_n-a_{n-1}=d$

The 6th term of an arithmetic sequence is 7,

 $u_6=7$ and the 10th term of the sequence is 23,  $u_{10}=23$  . What is the common difference of the sequence?

• 16

• 4

• 3

A comet is seen every 25 years. It was first seen in 1185. What part of this scenario is d, the common difference, and what part is the first term, $c_1$  ?

•  $d=25,\ c_1=1185$  

•  $d=1185,\ c_1=25$  

•  $d=47.4,\ c_1=1185$  

Using the explicit definition of an arithmetic sequence, $c_n=c_1+\left(n-1\right)d$  , with  $c_1=1185$  and d=25, figure out in what year was the comet seen for the fifth time?

• 1185

• 1210

• 1310

• 1285

A geometric sequence, $\left\{b_n\right\}$ , has the terms {5, 15, 45, 135,...}. Find the explicit definition for this sequence.  

•  $b_n=5\cdot3^{n-1}$  

•  $b_n=3\cdot5^{n-1}$  

•  $b_n=5+\left(n-1\right)3$  

Use this geometric sequence definition: $a_n=6\cdot2^{n-1}$  to find the 100th term

•  $3.80$  

•  $1.50\times10^5$  

•  $3.80\times10^{30}$