Material Taken From:

Mathematicsfor the international student

Mathematical Studies SL

Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce

Haese and Haese Publications, 2004

1) Find the general term un for an arithmetic sequence given that u3 = 8 and u8 = -17

Section 12CG – Arithmetic Sequences and Series

2) Insert four numbers between 3 and 12 so that all six numbers are in arithmetic sequence.

The sum of the n terms of an arithmetic series

12n n

nS u u

12 ( 1)2n

nS u n d

OR

3) Find the sum of 4 + 7 + 10 + 13 + … to 50 terms.

4) Find the sum of -6 + 1 + 8 + 15 + … + 141

5) The first five terms of an arithmetic sequence are shown below.2, 6, 10, 14, 18

(a) Write down the sixth number in the sequence.(b) Calculate the 200th term.

(c) Calculate the sum of the first 90 terms of the sequence.

A geometric sequence:

• occurs when each term can be obtained from the previous one by multiplying by the same non-zero constant.

»4, 12, 36, 108, …»125, 25, 5, 1, …

Section 12DG – Geometric Sequences and Series

Algebraic Definition:

{un} is geometric if (and only if) un + 1 = run

for all positive integers n where r is a constant (the common ratio)

The General Term of a geometric sequence

11

nnu u r

1) For the sequence 128, 4, 2, 1, ,....

a) Show that the sequence is geometricb) Find the general term un.c) Hence, find the 12th term as a fraction.

2) k – 1, 2k and 21 – k are consecutive terms of a geometric sequence. Find k.

3) A geometric sequence has u2 = -6 and u5 = 162. Find its general term.

4) Find the first term of the geometric sequence which

exceeds 1400. 6, 6 2, 12, 12 2,....

Homework

• Pg 404 – Section 12C–#8

• Pg 406-407 – Section 12D–#3, 4, 6bc, 7bd, 8b