M1T2: Lesson 3 Skills Practice - Determing Recursive & Explicit Expressions from Contexts

Determine whether each sequence is arithmetic or geometric. Then, write a recursive and the simplified explicit formula for the sequence.

4, 8, 16, 32, ...

The sequence is (arithmetic or geometric)

$a_{n}=a_{n-1}$

Explicit formula: $a_{n}=$

Determine whether each sequence is arithmetic or geometric. Then, write a recursive and the simplified explicit formula for the sequence.

$a_{1}=16, a_{2}=30, a_{3}=44, a_{4}=58, ...$

The sequence is (arithmetic or geometric)

$a_{n}=a_{n-1}$

Explicit formula: $a_{n}=$

Determine whether each sequence is arithmetic or geometric. Then, write a recursive and the simplified explicit formula for the sequence.

2, -6, 18, -54, ...

The sequence is (arithmetic or geometric)

$a_{n}=a_{n-1}$

Explicit formula: $a_{n}=$

Determine whether each sequence is arithmetic or geometric. Then, write a recursive and the simplified explicit formula for the sequence.

$a_{3}=7.3, a_{4}=9.4, a_{5}=11.5, a_{6}=13.6, a_{7}=15.7, ...$

The sequence is (arithmetic or geometric)

$a_{n}=a_{n-1}$

Explicit formula: $a_{n}=$

Determine whether each sequence is arithmetic or geometric. Then, write a recursive and the simplified explicit formula for the sequence.

320, 410, 500, ...

The sequence is (arithmetic or geometric)

$a_{n}=a_{n-1}$

Explicit formula: $a_{n}=$

Determine whether each sequence is arithmetic or geometric. Then, write a recursive and the simplified explicit formula for the sequence.

$a_{3}=63, a_{4}=189, a_{5}=567, a_{6}=1701, ...$

The sequence is (arithmetic or geometric)

$a_{n}=a_{n-1}$

Explicit formula: $a_{n}=$

Determine the specified terms of each sequence.

What is the 10th term of the sequence $a_{n}=3 \cdot 2^{n-1}?$

What is the 50th term of the sequence $a_{n}=100+(-8)(n-1)?$

What is the 6th term of the sequence$a_{n}=a_{n-1} \cdot (-3)$, if $a_{5}=162$?

What is the 12th term of the sequence$a_{n}=a_{n-1}+\frac{1}{3}$. if the 11th term is$\frac{17}{3}$?

What is the 23rd term of the sequence $a_{n}=a_{n-1}+2.3$, if the 21st term is 95.8?

What is the 19th term of the sequence $a_{n}=a_{n-1} \cdot (-\frac{1}{2}),$ if $a_{17}=162?$

Write an explicit formula to represent the sequence that models each scenario.

The population of a city started at 378,000. Every year thereafter it decreased by 23,000 individuals.

$a_{n}=$

A test showed that after the first hour of receiving a medication, 100 milligrams remained in the body. Continued tests showed that the dose found in the body halved every hour after the first hour.

$a_{n}=$

A new pet bakery sold 20 dog cakes during Week 1 of operation, 27 dog cakes during Week 2, and 34 dog cakes during week 3.

$a_{n}=$

A barrel starts with 6 cups of water in it. During a heavy rainstorm, the amount of water in the barrel doubles every minute.

$a_{n}=$

A petri dish starts with a sample of 3 bacteria. The number of bacteria triples every minute.

$a_{n}=$

Natalia is selling cupcakes at a bake sale. She starts with 100 cupcakes and sells 10 per hour.

$a_{n}=$

Write the explicit formula you can use to represent the terms of the sequence, then represent the sequence on the coordinate plane.

$a_{4}=\frac{3}{4},a_{5}=0,a_{6}=-\frac{3}{4},a_{7}=-1\frac{1}{2}$

$k_{8}=15,k_{9}=50,k_{10}=85,k_{11}=120$

The first term of the sequence is $m_{1}=\frac{1}{8}$ and the common ratio is -1.5.

$p_{2}=0.6,p_{3}=3.6,p_{4}=21.6,p_{5}=129.6$

The first term of the sequence is $m_{1}=\frac{1}{2}$ and the common difference is -20.

$p_{4}=-12,p_{5}=-4,p_{6}=-\frac{4}{3},p_{7}=-\frac{4}{9}$

Determine whether each given sequence is arithmetic or geometric. Then write the next 3 terms.

3, -12, 48, -192, ...

arithmetic or geometric?

next 3 terms:

2.$45,3.86,5.27,6.68,...$

arithmetic or geometric?

next 3 terms: