Question

List all the indicated terms of each finite sequence.
1. an = 4n - 5 for 1 ≤ n ≤ 5
2. an = n^3 - 1 for 1 ≤ n ≤ 4
3. an = 3n^2/2 for 1 ≤ n ≤ 5
4. an = n+3/2 for 1 ≤ n ≤ 3
5. an = n^4 - n^2 - 1 for 1 ≤ n ≤ 3
6. an = n/2 + n/3 for 1 ≤ n ≤ 3

Answer 1

Answer:

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Answer 2

Given:

1. an = 4n - 5 for 1 ≤ n ≤ 5

$\begin{array}{ll}a_{1}=4 \times 1-5=-1 & a_{2}=4 \times 2-5=3 \quad a_{3}=4 \times 3-5=7 \\a_{4}: 4 \times 4 \cdot 5=11 & a_{5}=4 \times 5-5=15\end{array}$

2. an = n^3 - 1 for 1 ≤ n ≤ 4

$\begin{array}{l}a_{1}=1^{3}-1=0 \quad a_{2}=2^{3}-1=7 \quad a_{3}=3^{3}-1=26 \\a_{4}=4^{3}-1=63\end{array}$

3. an = 3n^2/2 for 1 ≤ n ≤ 5

$\begin{array}{l}a_{1}=\frac{3}{2} \cdot 1^{2}=\frac{3}{2} \quad a_{2}=\frac{3}{2} \cdot 2^{2}=6 \quad a_{3}=\frac{3}{2} \cdot 3^{2}=\frac{27}{3} \\a_{4}=\frac{3}{2} \cdot 4^{2}=24 \quad a_{5}=\frac{1}{2} \cdot 5^{2}=\frac{x 5}{2}\end{array}$

4. an = n+3/2 for 1 ≤ n ≤ 3

$a_{1}=\frac{1+3}{2}=2 \quad a_{2}=\frac{2 t}{2}=\frac{5}{2} \quad a_{3}=\frac{3+3}{2}=3$

5. an = n^4 - n^2 - 1 for 1 ≤ n ≤ 3

$\begin{array}{l}a_{1}=1^{4}-1^{2}-1=-1 \quad a_{2}=2^{4}-2^{2}-1=9 \\a_{3}=3^{4}-3^{2}-1=71\end{array}$

6. an = n/2 + n/3 for 1 ≤ n ≤ 3

$\begin{aligned}a_{1}=\frac{1}{2}+\frac{1}{3}=\frac{5}{6} \quad a_{2}=\frac{2}{2}+\frac{2}{3}=\frac{5}{3} \\a_{3}=\frac{3}{2}+\frac{3}{3}=\frac{5}{2}\end{aligned}$