Sequences and Series

Question 1

How to find the first 6 numbers in an arithmetic/geometric series

Answer 1

Plug the number into n in the equation

Question 2

How to write a series using summation notation

Answer 2

Determine if it is arithmetic or geometric
Find the top number (the first number in the series)
Find the bottom number (usually one but whatever gets multiplied)
Make it equal to the generator

Question 3

How to write a rule for an arithmetic sequence

Answer 3

Find a1
Find r
Plug both into the formula an = a1 + (n-1)d

Question 4

How to find the nth term in an arithmetic sequence

Answer 4

Find the formula and plug the number in for n

Question 5

How to find the arithmetic rule with two equations

Answer 5

Solve both for a1
Use elimination to find the d
Plug d into the first equation
Write the equation with the formula an = a1 + (n-1)d

Question 6

How to find the sum of a arithmetic series(given i instead of n)

Answer 6

Plug all numbers into the equation Sn = n/2(a1+an)
Top number: n
a1: plug 1 into generator
an: plug n into the generator
Solve

Question 7

How to find the equation of a geometric sequence

Answer 7

Find a1
Find r
Plug them into the equation an= (a1) * (r)^n-1

Question 8

How to find the geometric rule with two equations

Answer 8

Solve both for a1
Make the two equal to each other and cross-multiply
Solve for a
Plug into equation
an = (a1) * (r)^n-1

Question 9

How to find the sum of a geometric series

Answer 9

Use equation Sn = (1-r^n/1-r)
Top number = n
Find r
Plug into equation and solve

Question 10

Arithmetic Series Equation

Answer 10

Sn = n/2(a1+an)

Question 11

Geometric Series Equation

Answer 11

Sn = (1-r^n/1-r)

Question 12

How to find the sum of an infinite geometric series

Answer 12

Use the equation S= (a1/1-r)
Find a1 and r

Question 13

Generator is ALWAYS

Answer 13

a1(r)^n-1

Question 14

If r is greater than 1…

Answer 14

The sum diverges

Question 15

How to find the first 6 terms of a recursive rule

Answer 15

Determine whether it is geometric or arithmetic
Use the equation an = a(n-1) +d or an = r(an-1)
Plug the previous equal to find the new one

Question 16

How to write the recursive rule of a sequence

Answer 16

Determine whether it is arithmetic or geometric
Find a1
Find d or r
Plug into either equation
A: a1= a1 an = an-1 + d
G: a1=a1 an = r(an-1)

Question 17

Arithmetic Explicit Rule

Answer 17

An = a1 + (n-1)d

Question 18

Arithmetic Recursive Rule

Answer 18

a1 = a1 An = an-1 + d

Question 19

Geometric Explicit Rule

Answer 19

An = a1 * r^n-1

Question 20

Geometric Recursive Rule

Answer 20

a1 = a1 An = r (an-1)

Question 21

True or False
Sequence has a sigma

Answer 21

False

Question 22

If there is no … at the end of a series, it is…

Answer 22

Not infinite and you have to find the upper limit which goes on top of the Sigma