Arithmetic Sequences and Arithmetic Series - Basic Intro

Multiple Choice

What is the sum of the first 8 terms of the geometric sequence: 1 , 3 , 9 , 27 , . . . ?

• 3,260

• 3,270

• 3,280

• 3,290

Multiple Choice

Find the next 3 terms of a geometric sequence 4, 24, 144, 864, . . .

• 1024, 4096, 16384

• 256, 1024, 4096

• 256, −1024, 4096

• 5184, 31,104, 186,624

Multiple Choice

Find the common ratio: 16, 8, 4, 2, . . .

• r = 2

• r = 8

• r = 1/4

• r= 1/2

Multiple Choice

What is the sum of the first ten terms of the sequence 4, -12, 36, -144 . . . ?

• 59,050

• -59,048

• -78,732

• 118,096

Multiple Choice

Find the sum of the geometric series.

2 + 12 + 72 + 432

• 432

• 518

• 211

• 438

Multiple Choice

It is the sum of the terms of the geometric sequence.

• geometric series

• arithmetic series

• fibonacci series

• harmonic series

Multiple Choice

Which sequence is represented by the equation 2(7)^n-1 ?

• 7, 14, 28, 56...

• 2, 14, 98, 686...

• 2, 9, 16, 23...

• 7,9,11,13...

Multiple Choice

Find S₈ for: -1 - 3 - 9 - 27...

• -3280

• -3135

• -3323

• -3343

Multiple Choice

Find the sum of the first 25 terms of the series: 6+14+22+30+...

• 450

• 2550

• 2650

• 550

Multiple Choice

Evaluate S₁₂ for the arithmetic series where:

a₁=?, a₁₂=48, and d=4

• 310

• 312

• 620

• 624

Multiple Choice

The sum of this arithmetic series is 595. a₁=28, and a_n=91. How many terms are there (what is n)?

• 9

• 10

• 11

• 12

Multiple Choice

What is the sum of the first 10 terms for the following geometric series:
1+1/2+1/4+1/8+1/16+...

• 0.999
• 0.002
• 9.8
• 1.998

Multiple Choice

Evaluate sum S₈:

a₁=?, a₈=839,808, r= -6

• 717456

• 719835

• 665624

• 668938

Multiple Choice

Describe the sequence, find the 5th term, and write the rule

-8, -6, -4, -2...

• geometric, a₅ = 2, a_n = 2n - 10

• geometric, a₅ = 0, a_n = -10n + 2

• arithmetic, a₅ = 2, a_n = -10n + 2

• arithmetic, a₅ = 0, a_n = 2n - 10

Multiple Choice

Identify the common difference.
97, 86, 75, 64, ...

• 8
• 11
• -11
• -8

Multiple Choice

Is the sequence 2, 4, 12, 48,... geometric?

• yes
• no

Multiple Choice

What type of series is
32 + 16 + 8 + 4 + 2 + 1

• Finite Arithmetic
• Finite Geometric
• Infinite Arithmetic
• Infinite Geometric

ARITHMETIC SERIES

It is the sum of the terms of the given arithmetic sequence.

ARITHMETIC SERIES

ARITHMETIC SERIES

ARITHMETIC SERIES

ARITHMETIC SERIES

PROBLEM SOLVING

PROBLEM SOLVING

Find the sum of all integers that are multiples of 4 from 1 to 150.

PROBLEM SOLVING

Find the sum of all integers that are multiples of 4 from 1 to 150.

PROBLEM SOLVING

Find the sum of all integers that are multiples of 4 from 1 to 150.

Since we have solve, how many terms or how many multiples of 4 are there from 1 to 150, and there are 37 terms. We can solve now the sum of the multiples of 4 from 1 to 150.

Multiple Select

Find the sum of the positive integers less than 150 but greater than 20 that are divisible by 7.

What are the formulas to be used to solve this problem?

• $$a_n=a_1+\left(n-1\right)d$$

• $$S_n=\frac{n}{2}\left[a_1+a_n\right]$$
  

Multiple Choice

You are sitting in row 23 and notice there are 65 seats in your row. The row in front of you has 63 seats and the row behind you has 67 seats. There are 42 rows in the auditorium. How many seats does the auditorium contain? (Hint: Find the number of seats in the first and last rows)

• 2,604
• 2,163
• 2,422
• 2,803

Multiple Choice

The n^th term of a geometric sequence is given by ...

Multiple Choice

The sum of an infinite Geometric series is given by:

Multiple Choice

List the first five terms of the geometric sequence. Assume that the sequence begins at n = 1.

• 1 , 3 , 6 , 9 , 12

• 3 , 9 , 27 , 81 , 243

• 0 , 1 , 3 , 9 , 27

• 1 , 3 , 9 , 27 , 81

Multiple Choice

List the first five terms of the geometric sequence. Assume that the sequence begins at n = 1.

• 2 , 1/2 , 1/8 , 1/32 , 1/128

• 1/2 , 1/8 , 1/32 , 1/128 , 1/256

• 8 , 2 , 1/2 , 1/8 , 1/32

• 2 , 8 , 32 , 128 , 256

Multiple Choice

The sequence 28, 34, 40, 46, 52, ..., 88 has 11 terms. Find the sum of the 11 terms.

• 550

• 638

• 610

• 288

Multiple Choice

Find the  $$a_n$$  Rule for the following sequence:

-4, -1, 2, 5, ...

• $$a_{n\ }=-4n\ +3$$  

• $$a_{n\ }=3n-4$$  

• $$a_{n\ }=3n-7$$  

• $$a_{n\ }=-3n\ +3$$  

• None of these are correct

Multiple Choice

Find 26th term in the arithmetic sequence: -15, -35, -55, -75, ...

• -515
• -490
• -535
• 460

Multiple Choice

For a certain arithmetic sequence,  $$d=4$$   and $$a_{30}=57.$$ What is a rule for the nth term of the sequence?

• $$a_n=-63-4n$$  

• $$a_n=-59-4n$$  

• $$a_n=-63+4n$$  

• $$a_n=-59+4n$$