Question

directions: write a possible explicit rule, then find $a_{10}$.11. ${-7, -6, -5, -4, -3, ...}$12. ${5, 7, 9, 11, 13, ...}$13. ${0, 7, 26, 63, 124, ...}$14. $left{\frac{1}{3}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{5}{7}, ...
ight}$

Explanation:

Step1: Identify sequence type (Q11)

This is an arithmetic sequence with first term $a_1=-7$, common difference $d=1$.
Explicit rule: $a_n = a_1 + (n-1)d = -7 + (n-1)(1) = n - 8$
Find $a_{10}$: $a_{10}=10-8=2$

Step2: Identify sequence type (Q12)

This is an arithmetic sequence with $a_1=5$, $d=2$.
Explicit rule: $a_n = 5 + (n-1)(2) = 2n + 3$
Find $a_{10}$: $a_{10}=2(10)+3=23$

Step3: Identify sequence type (Q13)

Terms follow $n^3 - 1$: $1^3-1=0$, $2^3-1=7$, $3^3-1=26$, etc.
Explicit rule: $a_n = n^3 - 1$
Find $a_{10}$: $a_{10}=10^3 - 1=1000-1=999$

Step4: Rewrite terms to find pattern (Q14)

Rewrite terms: $\frac{1}{3}, \frac{2}{4}, \frac{3}{5}, \frac{4}{6}, \frac{5}{7},...$. Numerator = $n$, denominator = $n+2$.
Explicit rule: $a_n = \frac{n}{n+2}$
Find $a_{10}$: $a_{10}=\frac{10}{10+2}=\frac{10}{12}=\frac{5}{6}$

Answer:

1. Explicit rule: $a_n = n - 8$; $a_{10}=2$
2. Explicit rule: $a_n = 2n + 3$; $a_{10}=23$
3. Explicit rule: $a_n = n^3 - 1$; $a_{10}=999$
4. Explicit rule: $a_n = \frac{n}{n+2}$; $a_{10}=\frac{5}{6}$