Gr12 Mathematics: Ch 1 Sum Number Patterns, Sequences and Series

<p>The average of the two numbers</p> Signup and view all the answers

<p>The sequence increases</p> Signup and view all the answers

<p>By subtracting consecutive terms</p> Signup and view all the answers

<p>To find the nth term of an arithmetic sequence</p> Signup and view all the answers

<p>Linear</p> Signup and view all the answers

<p>Tn = ar^(n-1)</p> Signup and view all the answers

<p>√ab</p> Signup and view all the answers

<p>The terms alternate in sign</p> Signup and view all the answers

<p>r = Tn / T(n-1)</p> Signup and view all the answers

<p>The sum of a specific number of terms of a sequence</p> Signup and view all the answers

<p>Sigma notation</p> Signup and view all the answers

<p>∑(i=m)^(n) T_i = T_m + T_{m+1} + ... + T_n</p> Signup and view all the answers

<p>The sum of infinitely many terms of a sequence</p> Signup and view all the answers

<p>An exponential graph</p> Signup and view all the answers

<p>Calculate the ratio between consecutive terms</p> Signup and view all the answers

<p>$S_n = \frac{a(1 - r^n)}{1 - r}$</p> Signup and view all the answers

<p>The constant value multiplied by the previous term to get the next term</p> Signup and view all the answers

<p>$-1 &lt; r &lt; 1$</p> Signup and view all the answers

<p>$S_\infty = \frac{a}{1 - r}$</p> Signup and view all the answers

<p>The difference between each term and the previous term</p> Signup and view all the answers

<p>$T_n = a + (n - 1)d$</p> Signup and view all the answers

<p>5050</p> Signup and view all the answers

<p>Pairing the numbers in ascending and descending order and adding the corresponding pairs</p> Signup and view all the answers

<p>$S_n = \frac{a(1 - r^n)}{1 - r}$</p> Signup and view all the answers

<p>S_n = (n / 2)(2a + (n - 1)d)</p> Signup and view all the answers

<p>To sum the arithmetic sequence from the first term to the last term</p> Signup and view all the answers

<p>$S_\infty = \frac{a}{1 - r}$</p> Signup and view all the answers

<p>S_n = a + (a + d) + (a + 2d) + ... + (l - 2d) + (l - d) + l</p> Signup and view all the answers

<p>$r &gt; 1$ or $r &lt; -1$</p> Signup and view all the answers

<p>S_n = (n / 2)(a + l)</p> Signup and view all the answers

<p>Tn = a + (n - 1)d</p> Signup and view all the answers

<p>The sequence forms a linear pattern when plotted on a graph</p> Signup and view all the answers

<p>Arithmetic mean</p> Signup and view all the answers

<p>$T_n = ar^{n-1}$</p> Signup and view all the answers

<p>Set the nth term equal to a specific value and solve for n</p> Signup and view all the answers

<p>To find the common difference</p> Signup and view all the answers

<p>Find the ratio between consecutive terms</p> Signup and view all the answers

<p>$S_n = rac{n}{2} (2a + (n - 1) d)$</p> Signup and view all the answers

<p>The sequence decays exponentially</p> Signup and view all the answers

<p>To calculate the sum of the first n terms of an arithmetic sequence.</p> Signup and view all the answers

<p>The terms form a linear pattern when plotted on a graph</p> Signup and view all the answers

<p>$S_n = rac{n}{2} (a + l)$</p> Signup and view all the answers

<p>A series</p> Signup and view all the answers

<p>It is given as a</p> Signup and view all the answers

<p>A straight line</p> Signup and view all the answers

<p>Sigma notation</p> Signup and view all the answers

<p>By summing the arithmetic sequence from the first term to the last term.</p> Signup and view all the answers

<p>A sum of infinitely many terms in a sequence</p> Signup and view all the answers

<p>$S_n = rac{n}{2} (a + l)$</p> Signup and view all the answers

<p>$\sum_{i=m}^{n} T_i = T_m + T_{m+1} + \cdots + T_{n-1} + T_n$</p> Signup and view all the answers

<p>To determine if the sequence is geometric</p> Signup and view all the answers

<p>An exponential graph</p> Signup and view all the answers

<p>The formula T_n = ar^(n-1)</p> Signup and view all the answers

<p>-1 &lt; r &lt; 1</p> Signup and view all the answers

<p>a(1 - r^n) / (r - 1)</p> Signup and view all the answers

<p>A series with a fixed number of terms</p> Signup and view all the answers

<p>a / (1 - r)</p> Signup and view all the answers

<p>A series where the number of terms goes to infinity</p> Signup and view all the answers

<p>To find the sum of a finite geometric series</p> Signup and view all the answers

<p>ar^(n - 1)</p> Signup and view all the answers

<p>A sequence where each term after the first is found by multiplying by a constant value</p> Signup and view all the answers

<p>n(a + l) / 2</p> Signup and view all the answers

<p>Writing the numbers in ascending and descending order and adding corresponding terms</p> Signup and view all the answers

<p>23</p> Signup and view all the answers

<p>2</p> Signup and view all the answers

<p>-11</p> Signup and view all the answers

<p>17</p> Signup and view all the answers

<p>3</p> Signup and view all the answers

<p>10</p> Signup and view all the answers

<p>20</p> Signup and view all the answers

<p>A straight line</p> Signup and view all the answers

<p>3/5</p> Signup and view all the answers

<p>a(1 - r^n)/(1 - r)</p> Signup and view all the answers

<p>An exponential curve</p> Signup and view all the answers

<p>r &lt; 1</p> Signup and view all the answers

<p>ar^(n-1)</p> Signup and view all the answers

<p>a/(1 - r)</p> Signup and view all the answers

<p>Alternating signs</p> Signup and view all the answers

<p>To represent the sum of terms in a sequence</p> Signup and view all the answers

<p>A finite series has a fixed number of terms, while an infinite series has an infinite number of terms</p> Signup and view all the answers

<p>√(ab)</p> Signup and view all the answers

<p>-1 &lt; r &lt; 1</p> Signup and view all the answers

<p>a(1 - r^n)/(1 - r)</p> Signup and view all the answers

<p>5050</p> Signup and view all the answers

<p>2</p> Signup and view all the answers

<p>a + (n - 1)d</p> Signup and view all the answers

<p>a/(1 - r)</p> Signup and view all the answers

<p>r &gt; 1 or r &lt; -1</p> Signup and view all the answers

<p>To calculate the sum of a finite series</p> Signup and view all the answers

<p>The terms increase by a constant value</p> Signup and view all the answers

<p>A straight line</p> Signup and view all the answers

<p>155</p> Signup and view all the answers

<p>S_n = (n/2) (a + l)</p> Signup and view all the answers

<p>420</p> Signup and view all the answers

<p>a = (2S_n) / n - (n-1)d</p> Signup and view all the answers

<p>S_n = (n/2) [2a + (n-1)d)]</p> Signup and view all the answers