Geometric sequences

Question 1

What is the nth term of a geometric sequence?

What are the three components?

Answer 1

un= a x r^n-1

RNA
Ratio
Number of terms
A first term

Question 2

What is a useful equation to set up in geometric sequences?

Answer 2

to find an unknown k/k-2 = 2k/k-4

Equalise two ways of getting the R value

Question 3

What is sn of a geometric sequence?

Answer 3

sn = a(1-r^n) / 1-r

Question 4

What is the sum to infinity of a geometric sequence?

What is important about this?

How to justify this in a question?

Answer 4

• a/ 1-r

The series must be convergent |r|<1

As s infinity is only valid for |r|<1 (nth term) < 1 for these values.

Question 5

How to prove that sn of geometric sequence?

Answer 5

-First write out sn
-Then write out rsn
Then subtract the two.
Then factor out sn

Question 6

How many terms in a sigma r notation?

Answer 6

-Upper limit - lower limit +1

Question 7

How to know whether the series is sum to infinity or sum to terms?

Answer 7

-If there is three dots at the end it is infinity.

Question 8

How do you deal with a question if money is being put in at the start of the month and then interest is being earned on this?

Answer 8

-Map out what is happening

Eg year 2 it will be 500 x 1.035 + 500 x 1.035
Then factor out 500 x (1.035)^n

Question 9

How to answer a question that for a trig geometric sequence explain why 0< theeta < pi/2 is a requirement for there to be a sum?

Answer 9

As the mod of r is less than 1 for the formula to work show show when cos2theta<1