Arithmetic & Geometric Sequences: Full Guide — Worksheet & Memo

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Grade 12 · Number Patterns, Sequences and Series

Arithmetic & Geometric Sequences: Full Guide

MEMORANDUM

Name:

Class:

Date:

Mark

/ 26

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
10th term of 3 ; 7 ; 11 ; … (arithmetic term)
(2)
a = 3, d = 4; T₁₀ = 3 + 9(4) = 39✓✓ (2)
2
8th term of 2 ; 5 ; 8 ; … (arithmetic term)
(2)
a = 2, d = 3; T₈ = 2 + 7(3) = 23✓✓ (2)
3
5th term of 3 ; 6 ; 12 ; … (geometric term)
(2)
a = 3, r = 2; T₅ = 3·2⁴ = 48✓✓ (2)
4
6th term of 1 ; 3 ; 9 ; … (geometric term)
(2)
a = 1, r = 3; T₆ = 3⁵ = 243✓✓ (2)
5
Which term of 4 ; 7 ; 10 ; … is 61? (which term)
(3)
4 + (n − 1)3 = 61 → n = 20✓✓✓ (3)
6
Which term of 2 ; 4 ; 8 ; … is 256? (which term)
(3)
2·2^{n − 1} = 256 → 2ⁿ = 256 → n = 8✓✓✓ (3)
7
Sum of the first 10 terms of 2 ; 4 ; 6 ; … (arithmetic sum)
(3)
S₁₀ = 10/2[2(2) + 9(2)] = 5(22) = 110✓✓✓ (3)
8
Sum of the first 15 terms of 3 ; 5 ; 7 ; … (arithmetic sum)
(3)
S₁₅ = 15/2[6 + 14(2)] = 15/2(34) = 255✓✓✓ (3)
9
Sum to infinity of 6 + 3 + 1,5 + … (S∞)
(3)
r = 1/2; 6/(1 − 1/2) = 12✓✓✓ (3)
10
Sum to infinity of 10 + 2 + 0,4 + … (S∞)
(3)
r = 0,2; 10/(1 − 0,2) = 10/0,8 = 12,5✓✓✓ (3)

TOTAL: 26 marks