Calculate
      Â
The sum given in part (a) is an arithmetic series.
Write down the first term and the common difference.
Did this page help you?
Calculate
      Â
The sum given in part (a) is an arithmetic series.
Write down the first term and the common difference.
Did this page help you?
Calculate
      Â
The sum given in part (a) is a geometric series.
Write down the first term and the common ratio.
Did this page help you?
It is given that
      Â
where  is a positive integer.Â
Determine if the series is arithmetic or geometric, justifying your answer.
Did this page help you?
A Fibonacci sequence can be expressed as the following recurrence relation
        Â
Write down the first six terms of the Fibonacci sequence with .
Find
      Â
withÂ
Did this page help you?
A sequence is defined by the recurrence relation .
Write down the first five terms of the sequence.
Determine if the sequence is arithmetic or geometric, justifying your answer.
Find
      Â
Did this page help you?
The term of an arithmetic series is given by .
Write the sum of the series, up to the  term, in sigma notation.
The term of a geometric series is given by .
Write the sum of the series, up to the  term, in sigma notation.
Did this page help you?
Given that
         Â
determine the value of .
Did this page help you?
A sequence is defined for  by the recurrence relation  withÂ
Calculate
         Â
What value of would make every term of the sequence equal?
Find the range of values for that would ensure every term of the sequence is positive?
Did this page help you?
The first terms of a series are given by .
Show that this is an arithmetic series, and determine its first term and common difference.
Given that   ,
Did this page help you?
The first  terms of a series are given by .
Show that this is a geometric series, and determine its first term and common ratio.
Given that = 20470,
Show thatÂ
For this value of , calculate .
Did this page help you?
A geometric series is given byÂ
Did this page help you?
An arithmetic series is given byÂ
Given that and , find the values of  and .
Did this page help you?
A sequence is defined for by the recurrence relation Â
Calculate
   Â
Did this page help you?
A sequence is defined for by the recurrence relationÂ
Calculate, giving your answers as exact valuesÂ
  Â
Did this page help you?
A sequence is defined for by the recurrence relationÂ
where  is a constant.
Write down expressions for and  in terms of .
Given that the sequence is periodic with order 2, and given as well that ,
Find the value of .
For the value of  found in part (b)
CalculateÂ
Did this page help you?
The terms of a sequence are defined by  for all .
State, with a reason, whether this sequence is increasing, decreasing, or neither.
It can be shown that, for all ,
        Â
Using that formula,
CalculateÂ
Find the value of ,i.e. the sum of the squares of all the integers between 51 and 100 inclusive.
Did this page help you?
Given that ,Â
Did this page help you?
Given that and , find the values of andÂ
Did this page help you?
Given that ,
Show thatÂ
For this value of , calculate .
Did this page help you?
A convergent geometric series is given byÂ
Write down the range of possible values of .
Given that  =24
Calculate the value of .
Did this page help you?
A sequence is defined for by the recurrence relation Â
Calculate
Did this page help you?
A sequence is defined for by the recurrence relation Â
Calculate, giving your answers as exact values
Â
Did this page help you?
A sequence is defined for by the recurrence relationÂ
where  is a constant.
Given that the sequence is periodic with order 2, and given as well that ,
Find the value of .
For the value of  found in part (a),
Calculate Â
Did this page help you?
The terms of a sequence are defined, for all  by .
State, with a reason, whether this sequence is increasing, decreasing, or neither.
It can be shown that, for all ,
            =   and         Â
Using those formulas,
Show that .
Did this page help you?
Given that , find the value of .
Did this page help you?
Given that , Â
For this value of , calculate .
Did this page help you?
Given that , and , find the values of  and .
Did this page help you?
A convergent geometric series is given by , where in all cases the square root symbol indicates the positive square root of the number in question.
Write down the range of possible values of .
Given thatÂ
Calculate the value of .
Did this page help you?
A sequence is defined for by .
Calculate , giving your answer as an exact value.
Did this page help you?
A sequence is defined for all  by
        Â
Determine, giving reasons for your answer, whether the sequence is increasing, decreasing, or neither.
A different sequence is defined for all byÂ
where  is a real constant.
Given that the sequence is not periodic,
suggest a possible value for , giving a reason for your answer.
Did this page help you?
A sequence is defined for by the recurrence relation Â
where  and  are real numbers.
Show that the sequence is periodic, and determine its order.
Given that and Â
determine the possible values of  and .
Did this page help you?
Prove that, for all ,
       Â
Â
Did this page help you?