Answer:
The missing two terms are -41 and -52
a. The sequence is arithmetic
b. The explicit formula for the sequence is [tex]a_{n}=3-11n[/tex]
c. The recursive formula for this sequence is [tex]a_{1}[/tex] = -8; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + -11
d. The 30th term is -327
Step-by-step explanation:
The terms of the sequence are -8 , -19 , -30
∵ -19 - (-8) = -19 + 8 = -11
∵ -30 - (-19) = -30 + 19 = -11
- That means there is a constant difference between each two
consecutive terms
∴ -30 + -11 = -41
∴ -41 + -11 = -52
∴ The missing two terms are -41 and -52
a.
∵ There is a constant difference between each two
consecutive terms
∴ The sequence is arithmetic
b.
The explicit formula of the nth term of an arithmetic sequence is [tex]a_{n}=a+(n-1)d[/tex], where a is the first term and d is the constant difference between each two consecutive term
∵ The first term is -8
∴ a = -8
∵ The constant difference is -11
∴ d = -11
- Substitute them in the formula above
∴ [tex]a_{n}=-8+(n-1)(-11)[/tex]
- Simplify it by multiplying (n - 1) times -11
∴ [tex]a_{n}=-8-11n+11[/tex]
∴ [tex]a_{n}=3-11n[/tex]
∴ The explicit formula for the sequence is [tex]a_{n}=3-11n[/tex]
c.
The recursive formula of the arithmetic sequence is:
[tex]a_{1}[/tex] = first term; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d, where d is the common difference between each two consecutive terms
∵ The first term is -8
∴ [tex]a_{1}=-8[/tex]
∵ The constant difference is -11
∴ d = -11
∴ [tex]a_{1}[/tex] = -8; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + -11
∴ The recursive formula for this sequence is [tex]a_{1}[/tex] = -8; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + -11
d.
∵ The term is 30th
∴ n = 30
- Substitute it in the explicit formula of the sequence
∴ [tex]n_{30}=3 - 11(30)[/tex]
∴ [tex]n_{30}=3 - 330[/tex]
∴ [tex]n_{30}=-327[/tex]
∴ The 30th term is -327
