Arithmetic & Geometric Sequences: Full Guide — Worksheet & Memo

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Grade 12 · Patterns & Sequences

Arithmetic & Geometric Sequences: Full Guide

MEMORANDUM

Name:

Class:

Date:

Mark

/ 20

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)
(2)
4+(n−1)3 = 61 → n = 20✓✓ (2)
6
Which term of 2, 4, 8, … is 256? (which term)
(2)
2·2ⁿ⁻¹ = 256 → 2ⁿ = 256 → n = 8✓✓ (2)
7
Sum of the first 10 terms of 2, 4, 6, … (arithmetic sum)
(2)
S₁₀ = 102[2(2)+9(2)] = 5(22) = 110✓✓ (2)
8
Sum of the first 15 terms of 3, 5, 7, … (arithmetic sum)
(2)
S₁₅ = 152[6+14(2)] = 152(34) = 255✓✓ (2)
9
Sum to infinity of 6 + 3 + 1,5 + … (S∞)
(2)
r = 12; 6/(1−12) = 12✓✓ (2)
10
Sum to infinity of 10 + 2 + 0,4 + … (S∞)
(2)
r = 0,2; 100.8 = 12,5✓✓ (2)

TOTAL: 20 marks