No questions found
(a) Calculate the 8th term $(F_8)$ and the 9th term $(F_9)$.
$F_8 = \text{..................................................}$
$F_9 = \text{..................................................}$
(b) Complete the table.
$$\begin{array}{cccc} F_1 & = & 5 & \\ F_1 + F_2 & = & 5 + 3 & = & 8 \\ F_1 + F_2 + F_3 & = & 5 + 3 + 8 & = & 16 \\ F_1 + F_2 + F_3 + F_4 & = & \text{........................} & \text{........} \\ \hline F_3 - F_2 & = & 8 - 3 & = & 5 \\ F_4 - F_2 & = & \text{................} & \text{..........} \\ F_5 - F_2 & = & \text{................} & \text{..........} \\ \end{array}$$
(c) Use what you notice in the table in part (b) to complete this statement.
$F_1 + F_2 + F_3 + F_4 + F_5 = F_{\text{......}} - F_{\text{......}}$
(d) Use the statement in part (c) to complete this general statement.
$F_1 + F_2 + F_3 + \cdots + F_n = F_{n + \text{..........}} - F_{\text{......}}$
(e) Show that your statement in part (d) is correct when $n = 7$.
588
519
597
In another F-type sequence the first term is 3 and the second term is 1.
(a) Complete the first five terms.
3, 1, ........ , ........ , ........ [2]
(b) Is your statement in Question 1(c) correct for the sum of the first five terms in this sequence?
............................................................................................................................................................................................................................................................................ [3]
582
569
541
In another F-type sequence the 2nd term is 3 and the 12th term is 652. Use your answer to Question 1(d) to find the sum of the first 10 terms.
554
560
556
In another F-type sequence the first term is 6 and the second term is $k$.
(a) Find an expression, in terms of $k$, for the 4th term. Write your answer in its simplest form. ....................................................... [2]
(b) The 4th term of this sequence is 14. Find $k$ and complete the first four terms.
6, ........ , ........ , 14 [3]
516
561
572
An F-type sequence has five terms.
(a) There is a relationship between the middle term and the sum of the 1st term and the 5th term.
Investigate this relationship by making up at least three numerical examples of F-type sequences.
Write down this relationship.
........................................................... [6]
(b) In another F-type sequence the first term is \(x\) and the second term is \(y\).
(i) Find, in its simplest form, an expression in terms of \(x\) and \(y\) for the 5th term.
........................................................... [3]
(ii) Use algebra to show that the relationship in part (a) is correct.
........................................................... [2]
522
514
517
