Gegee die volgende kwadratiese ry: -2; 0; 3; 7; .. - English General - NSC Mathematics - Question 2 - 2016 - Paper 1

To determine the n^e term, we recognize that the sequence can be represented as:

$T_n = a + (n - 1)d$

where $a$ is the first term and $d$ the common difference. With the first term $T_1 = -2$ and the pattern of differences, we derive: $T_n = -2 + (n - 1) * 3 = -2 + 3n - 3 = 3n - 5.$

Setting the expression from part 2.1.2 equal to 322, we have:

$3n - 5 = 322$

Solving for n:

$3n = 322 + 5$ $3n = 327$ $n = 109.$ Thus, the 109^e term of the sequence equals 322.

Given the arithmetic sequence where the second term is 8 and the fifth term is 10, we can establish that the common difference $d$ is given by:

$a + d = 8$ $a + 4d = 10.$ Subtracting these, we find $3d = 2 o d = \frac{2}{3}.$

The sum of an arithmetic series can be calculated with the formula:

$S_n = \frac{n}{2} (2a + (n-1)d)$

Here, substituting the values: $n = 50$, $a = 8$, and using $d = \frac{2}{3}$:

$S_{50} = \frac{50}{2} (2 \times 8 + 49 \times \frac{2}{3}) = 25(16 + \frac{98}{3}) = 25(\frac{48 + 98}{3}) = 25 \times \frac{146}{3} = \frac{3650}{3}.$

Continuing from the previous calculation, we find that the derived sum of the first 50 terms was computed to yield: S_{50} = \frac{3650}{3}.\ Therefore, the final answer is confirmed.