Question 7 of 10Identify the explicit function for the sequence in the table.x y1 72 193 314 435 55A.a(n) = 12 + (n − 1) • 7B.a(n) = 7(n − 1)C.a(n) = 7 + (n − 1) • 12D.a(n) = 12(n − 1)

Question 1 of 10The values in the table represent a linear function. What is the common difference of the associated arithmetic sequence?x y1 72 263 454 645 83A.24B.38C.19D.1

The sequence 5, 7, ______, 11 ...... n is an arithmetic progressionQuestion 9Answera.6b.9c.3d.10

From the previous question, for what values of n is the number 7 appended to list a. 7 6 8 9

NO1n f(n)1 32 133 234 335 4367a) Complete the table.b) Express in words the pattern you observed.c) Find a general formula for your pattern in terms of n.d) Verify your formula.e) Test and justify your formula.

Page 2 of 111. Here are the first five terms in a number sequence.7 10 13 16 19(a) Find the 10th term in this number sequence..........................(2)(b) Write an expression, in terms of n, for the nth term of this number sequence..........................(2)2. A number sequence has nth term 6n + 3(a) Write down the first four terms of this sequence.1st term ..............., 2nd term ..............., 3rd term ..............., 4th term ...............(3)(b) Sara says that 1008 is a term in this sequence.Explain why she is wrong.................................................................................................................................................................................................................................................................................................................................................................................................(1)Page 3 of 113. A sequence of numbers is shown below.1 5 9 13 17 ... ...(a) Find an expression for the nth term of the sequence..........................(2)(b) Explain why 95 will not be a term in this sequence.................................................................................................................................................................................................................................................................(2)4. The nth term of a number sequence is given by 5n + 2(a) Work out the first three terms of the number sequence.1st term ..............., 2nd term ..............., 3rd term ...............(2)Here are the first five terms of another number sequence.5 11 17 23 29(b) Find, in terms of n, an expression for the nth term of this sequence..........................(2)Page 4 of 115. A sequence of numbers is shown.2 9 16 23 30 ... ...(a) Find an expression for the nth term of the sequence..........................(2)(b) Find the 100th term in the sequence..........................(2)6. The nth term of a number sequence is n2 + 3.(a) Find the first three terms of this sequence.1st term ..............., 2nd term ..............., 3rd term ...............(2)(b) Work out the difference between the 5th and 10th terms in the sequence..........................(3)Page 5 of 117. The first 5 terms in a number sequence are10 7 4 1 −2 ... ...(a) Work out the nth term of the sequence..........................(2)(b) Find the 50th term of the sequence..........................(2)8. Work out the nth term for this sequence12 22 32 42 52 ... ............................(2)Page 6 of 119. The nth term of a sequence is 3n − 2(a) Write down the first two terms of this sequence.1st term ..............., 2nd term ...............(2)(b) Which term of the sequence is equal to 70?.........................(2)(c) Explain why 101 is not a term in the sequence.................................................................................................................................................................................................................................................................................................................................................................................................(2)Page 7 of 1110. Here are the nth terms of 4 sequences.Sequence 1 nth term 3n + 1Sequence 2 nth term 5n + 10Sequence 3 nth term 10nSequence 4 nth term 5n - 1For each sequence state whether the numbers in the sequence areA Always multiples of 5S Sometimes multiples of 5N Never multiples of 5Sequence 1 ....................Sequence 2 ....................Sequence 3 ....................Sequence 4 ....................(4)Page 8 of 1111. The nth term of a sequence is 5 − 3nWrite down the first three terms of the sequence.1st term ..............., 2nd term ..............., 3rd term ...............(2)12. The nth term of a sequence is 4n − 7(a) Write down the first three terms of the sequence.1st term ..............., 2nd term ..............., 3rd term ...............(2)(b) What is the difference between the 50th and 51st terms?....................(1)The last term of this sequence is 393.(c) How many terms are there in this sequence?....................(2)Page 9 of 1113. Find the nth term of the sequences(a) 1, 4, 9, 16, 25, .......................(1)(b) 3, 6, 11, 18, 27, .......................(1)(c) −3, 0, 5, 12, 21, .......................(1)(d) 2, 8, 18, 32, 50, .......................(1)14. The first 5 terms in a number sequence are30 25 20 15 10 ... ...Work out the nth term of the sequence..........................(2)Page 10 of 1115. The first 5 terms in a number sequence are2 2.5 3 3.5 4 ... ...(a) Work out the nth term of the sequence..........................(2)(b) Work out the 20th term of the sequence..........................(2)16. Martin has written the first 50 terms of the sequence with nth term 150 − 4n.Work out which term is the first negative term..........................(3)Page 11 of 1117. The nth term of a sequence is (n + 1)(n + 3)Work out the first three terms of the sequence.1st term ..............., 2nd term ..............., 3rd term ...............(2)