Arithmetic and Geometric Sequences

Arithmetic, Geometric or Neither

100

Is 4,6,7,20, ...?

What is neither.

200

45,50,55,60, ...?

What is arithmetic.

300

2, 4, 8, 16, ...?

What is geometric.

400

1/27, 1/81, 1/243, ...?

What is geometric.

500

66,87.5,109,130.5,...?

What is arithmetic .

Terminology

100

This represents the first term of a sequence U_n 

       

What is U₁

200

This represents the number of terms in a sequence.

What is n?

300

The variable r in a geometric sequence represents this.

What is the common ratio?

400

If a question asks for U_8, what is it asking for?

What is the 8th term.

500

The constant that is added to any term to get the next term in an arithmetic sequence.

What is a common difference.

Equation for Arithmetic

100

Write the explicit form of the sequence 4,5,6,7.

What is U_n=n+3

200

Write the explicit form of the sequence 7,5,3,1.

 What is U_n=-2n+9

300

Write the explicit form of the sequence 66,78,90,102.

What is U_n = 12n+54

400

Write the explicit form of the sequence 32,43,54,65,76.

t_n = 32 + (n-1)11

What is t_n=11n+21

500

The formula that will allow you to get any term of a sequence.

What is What is explicit?

Equation for geometric

100

U₁=5, r=2

What is 5(n)^n-1

200

U₁=4, r=1/4

What is U_n= 4(1/4)^n-1

300

{3, 9, 27, 81,...}

What is U_n=3(3)^n-1

400

{5, 10, 20, 40, ...}

What is U_n=5(2)^n-1

500

U₂=192, and U₇=6

What is U_n=384(1/2)^n-1

Word Problems

100

A movie theater shown has 30 seats in the first row. Each row behind the first row gains two additional seats. How many seats are in the 5th row in the center section?

What is there are 38 seats in the 5th row.

200

Milo wants to build a pyramid out of legos. He starts with 8 legos in the base, 7 on the next layer, 6 on the nest and so on. What layer will only have one lego?

What is layer 8 will have only 1 lego.

300

A writer wrote 890 words on the first day, 760 words on the second day and 630 words on the third day, and so on in an arithmetic sequence. How many words did the writer write on the 7th day?

What is they will write 110 words on the 7th day.

400

After knee surgery our doctor tells you to slowly increase your running time. You should run 12 minutes each day the first week and each week after increase the time by 6 minutes per day. How many weeks will it be before you run 60 minutes per day?

What is it will be 9 weeks before you run 60 minutes each day.

500

There are 130 students in grade one, 210 students in grade two and 290 students in grade three, and so on to grade six in an arithmetic sequence. What’s the total amount of students in the elementary school?

What is there are 1980 students in the elementary school.