Everything Maths Grade 12

3.6 CHAPTER 3. SEQUENCES AND SERIES for an arithmetic sequence and sum it from i = 1 to any positive integer n: �n i=1 ai = �n i ...

CHAPTER 3. SEQUENCES AND SERIES 3.7 The common difference of an arithmetic series is 3. Calculate the value of n for which the ...

3.8 CHAPTER 3. SEQUENCES AND SERIES k = 1 : 23 − 13 = 3(1)^2 + 3(1) + 1 k = 2 : 33 − 23 = 3(2)^2 + 3(2) + 1 k = 3 : 43 − 33 = 3( ...

CHAPTER 3. SEQUENCES AND SERIES 3.8 By simply adding together the first n terms, we are actually writing out the series Sn= a 1 ...

3.9 CHAPTER 3. SEQUENCES AND SERIES 3.9 Infinite Series EMCAB Thus far we have beenworking only with finite sums, meaning that w ...

CHAPTER 3. SEQUENCES AND SERIES 3.9 Therefore, Sn = a 1 (rn− 1) r− 1 S∞ = a 1 (0− 1) r− 1 for− 1 < r < 1 = −a 1 r− 1 = a 1 ...

3.9 CHAPTER 3. SEQUENCES AND SERIES Is 1 + 2 + 3 + 4 +··· an example of a finite series or an infinite series? Calculate �^6 k ...

CHAPTER 3. SEQUENCES AND SERIES 3.9 (a) What is the annual increase if, over 20 years, he would have received a total of R143 50 ...

3.9 CHAPTER 3. SEQUENCES AND SERIES Observe the patternbelow: A B B B C C C C C D D D D D D D E E E E E E E E E (a) If the pat ...

Finance 4 4.1 Introduction EMCAD In earlier grades simpleinterest and compoundinterest were studied, together with the concept o ...

4.3 CHAPTER 4. FINANCE Example 1: Term of Investment - Logarithms QUESTION Suppose we invested R3 500 into a savings account whi ...

CHAPTER 4. FINANCE 4.3 after three years, how much do I need to initiallyput into a bank accountearning 10% p.a. to be able to a ...

4.3 CHAPTER 4. FINANCE Present Values of a Series of Payments EMCAH So having reviewed themathematics of sequences and series, y ...

CHAPTER 4. FINANCE 4.3 can be re-written as follows, using what we knowfrom Chapter 3 of this text book: v^1 +v^2 +v^3 +··· +vn ...

4.3 CHAPTER 4. FINANCE Example 2: Monthly mortgage repayments QUESTION Sam is looking to buy his first flat, and has R15 000 in ...

CHAPTER 4. FINANCE 4.3 That means that to buya flat for R250 000, after Sam pays a R15 000 deposit, he will make repayments to t ...

4.3 CHAPTER 4. FINANCE X× 1 − (1 + 0,75%)−^240 0 ,75% = R190 000 X× 111 ,14495 = R190 000 X = R1 709, 48 Step 4 : Write the fina ...

CHAPTER 4. FINANCE 4.3 Future Value of a Seriesof Payments EMCAI In the same way that when we have a single payment, we can calc ...

4.4 CHAPTER 4. FINANCE So if we want to use our numbers, we know that A =R45 000, n = 24 (because we are looking at monthly paym ...

CHAPTER 4. FINANCE 4.4 Loan Schedules EMCAK So far, we have been working out loan repayment amounts by taking all the payments a ...