19.c Sequences

Question 1

What is a “sequence”?

Answer 1

An ordered list of numbers in which the order of the numbers is explained by a formula

Question 2

How can you find the first term of a sequence?

Answer 2

Plug in 1 for n into the function

Question 3

What is the notation used for sequences?

Answer 3

Where n denotes which term number it is

(does not need to be “a”, can be anythign really)

Question 4

Solve:

Answer 4

Question 5

What is a recursive formula?

Answer 5

When a formula is recursive, the nth term is given in terms of its previous term or terms.

Question 6

Find the equivalent recursive formula:

Answer 6

Question 7

What is an arithmetic sequence?

Answer 7

A sequence in which the difference between every pair of two consecutive terms is the same.

Question 8

What is the formula of an arithmetic sequence?

Answer 8

where:
d is the common difference
a1 is the first term of the squence

Question 9

What is the formula used to calculate the sum of an arithmetic sequence?

Answer 9

Question 10

When tick marks on a GMAT question are evenly spaced, the difference is _______________

Answer 10

When tick marks on a GMAT question are evenly spaced, the difference is CONSTANT

Question 11

Find k

Answer 11

= 47

Question 12

How would you solve this?

Answer 12

Question 13

Solve:

Answer 13

Question 14

What is a “geometric sequence”?

Answer 14

One in which the ratio between every pair of two consecutive terms is the same.

Question 15

What is the formula for “geometric sequence”?

Answer 15

where:
a1 = first term
r = common ratio

Question 16

What is the “common ratio”?

Answer 16

The ratio between every pair of two consecutive numbers in a GEOMETRIC SEQUENCE

Question 17

Solve:

Answer 17

Question 18

Solve for the sum of a repeating sequence:

Answer 18

FIND THE PATTERN!!!

and then add!

Question 19

How do you determine the sum from this?

Answer 19

Cancel fractions adding to zero

Question 20

Solve:

Answer 20

Calculate some of the first terms, some of the last terms… and see whether they cancel out