Question

write each arithmetic series in sigma notation. the lower bound is given.

1. \\(6 + 12 + 18 + \cdots + 66\\); \\(n = 1\\)
2. \\(-1 + 0 + 1 + \cdots + 7\\); \\(n = 1\\)
3. \\(17 + 21 + 25 + \cdots + 61\\); \\(n = 4\\)
4. \\(1 + 0 + (-1) + (-2) + \cdots + (-13)\\); \\(n = 6\\)
5. \\(-\frac{13}{5} + \left(-\frac{12}{5}\

ight) + \left(-\frac{11}{5}\
ight) + \cdots + \left(-\frac{3}{5}\
ight)\\); \\(n = 2\\)

1. \\(9.25 + 8.5 + 7.75 + \cdots - 2\\); \\(n = 1\\)

Explanation:

Find the general term and upper bound for Question 63

$$
LATEXBLOCK0
$$

Find the general term and upper bound for Question 64

$$
LATEXBLOCK1
$$

Find the general term and upper bound for Question 65

$$
LATEXBLOCK2
$$

Find the general term and upper bound for Question 66

$$
LATEXBLOCK3
$$

Find the general term and upper bound for Question 67

$$
LATEXBLOCK4
$$

Find the general term and upper bound for Question 68

$$
LATEXBLOCK5
$$

Answer:

Question 63

$$\sum_{k=1}^{11} 6k$$

Question 64

$$\sum_{k=1}^{9} (k - 2)$$

Question 65

$$\sum_{k=4}^{15} (4k + 1)$$

Question 66

$$\sum_{k=6}^{20} (7 - k)$$

Question 67

$$\sum_{k=2}^{12} \frac{k - 15}{5}$$

Question 68

$$\sum_{k=1}^{16} (10 - 0.75k)$$