Arithmetic & Geometric Sequences: Full Guide — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 12 · Patterns & Sequences

Arithmetic & Geometric Sequences: Full Guide

EXAM-STYLE CLASS TEST

Marks

Duration

50 minutes

Questions

Name:

Class:

Date:

Mark

/ 33

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
T_n = a + (n − 1)d is the general term of …
(1)
A)an arithmetic sequence
B)a geometric sequence
C)a quadratic pattern
D)a convergent series
1.2
The 20th term of 7 ; 11 ; 15 ; … is …
(1)
A)83
B)80
C)87
D)76
1.3
The common ratio of 3 ; 6 ; 12 ; … is …
(1)
A)2
B)3
C)6
D)12
1.4
The 8th term of 3 ; 6 ; 12 ; … is …
(1)
A)384
B)192
C)768
D)24
1.5
The sum of the first 20 terms of 7 ; 11 ; 15 ; … is …
(1)
A)900
B)830
C)1 800
D)90
1.6
In an arithmetic sequence T₅ = 17 and T₉ = 33. Then d = …
(1)
A)4
B)16
C)2
D)8
1.7
A geometric SERIES converges when …
(1)
A)−1 < r < 1
B)r > 1
C)r = 1
D)r < 0
1.8
The sum to infinity of 8 + 4 + 2 + … is …
(1)
A)16
B)14
C)8
D)32
1.9
In a geometric sequence T₃ = 20 and T₅ = 80. The POSITIVE value of r is …
(1)
A)2
B)4
C)60
D)√60
1.10
The sum of the first n terms of a GEOMETRIC series (r − 1 is not 0) is …
(1)
A)a(rⁿ − 1)r − 1
B)a(rⁿ + 1)r − 1
C)n2[2a + (n − 1)d]
D)a1 − r

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[11 MARKS]

In an ARITHMETIC sequence the third term is 11 and the seventh term is 27.

2.1
Determine the common difference d.
(3)
2.2
Determine the first term a.
(2)
2.3
Calculate the sum of the first 20 terms.
(3)
2.4
Determine which term of the sequence is equal to 99.
(3)

Question 3

[12 MARKS]

In a GEOMETRIC sequence the second term is 6 and the fifth term is 48.

3.1
Determine the constant ratio r.
(4)
3.2
Determine the first term.
(2)
3.3
Calculate the sum of the first 8 terms.
(3)
3.4
Explain why this series does NOT have a sum to infinity, and give an example of a geometric series that does.
(3)

TOTAL: 33 marks

This question paper consists of 3 questions.