Unit 3- Growth and Decay in Sequences

Question 1

What is an arithmetic sequence?

Answer 1

An arithmetic sequence is one where there is a common difference (d) between consecutive terms.

It goes from one term to the next by always adding or subtracting the same constant value.

Question 2

How do you find d?

Answer 2

d=tn+1 - tn

(a term minus the term before it)

Question 3

What is the recurrence relation for arithmetic sequences?

Answer 3

tn+1= tn + d

(very similar to a recurrence relation of loans)

Question 4

What is the nth term and its fomula?

Answer 4

If a question asks after a certain period of time? and you’re skipping a lot of terms and its not like a recurrence relation with each term in order.

t1+ (n-1) d

Question 5

What is the general term of an arithmetic sequence?

Answer 5

Like in investments, this is different to a recurrence relation, where instead of doing each one in order, you’re finding specific values from the formula.

tn =t1 + (n-1) d

Question 6

If the start of an arithmetic sequence is one where the t value can start at 0 (e.g. in money its appropriate to start at 0)

What formula do you use for this?

Answer 6

tn=t0 + nd

Question 7

What is a geometric sequence?

Answer 7

A geometric is one where there is a common ratio (r) between consecutive terms.

This is generated by multiplying each term by a constant factor to find the next term in the sequence.

Question 8

What is the recurrence relation for a geometric sequence?

Answer 8

tn+1 = tn times r

Question 9

What is the general formula for a geometric sequence?

Answer 9

(tn)=(t1)r^n-1

Question 10

How do you find the ratio for a geometric formula?

Answer 10

r= (tn+1)/(tn)