Arithmetic and geometric sequences

What is an arithmetic sequence?

The difference between consecutive terms are constant

What are arithmetic sequences also sometimes known as?

Arithmetic progressions

What is the nth term for an arithmetic sequence?

Un= a + (n-1)d

What is a?

The first term

What is Un?

The nth term

What is n?

The term

What is d?

The common difference

What is a geometric sequence?

Sequence that has a common ratio between consecutive terms

What is a geometric sequence sometimes also known as?

Geometric progression

What happens with a geometric sequence that has a common ratio IrI <1

It converges- tends to a certain value which is the limit of the sequence

What is an alternating sequence?

A sequence in which terms are alternately positive and negative

What is the nth term for a geometric sequence?

Un= ar to the power of n-1

What is a?

The first term

What is r?

The common ratio

How would you find the first term in a sequence that is negative?

Set Un< 0

How could you calculate the common ratio between consecutive terms in a geometric sequence?

Using U2/U1 = U3/U2

How would you show a number using a sequence?

eg: is 1071 in this sequence?

Work out the nth term

Put the nth term equal to the number (eg 1071)

Rearrange to calculate n, if n is an integer it is in the sequence

How do you calculate how many terms are in a sequence?

Work out the nth term

Put the last number equal to the nth term

Rearrange to calculate n

How do you calculate what is the first term to exceed a number?

Work out the the nth term

Set the nth term as > the number

Rearrange to have n >

If you are given the first three terms of a geometric sequence algebraically, how do you calculate the values?

Calculate the common ratio using U2/U1 = U3/U2

Then, multiply both sides by the denominators

Then solve quadratic