Answer:
Step-by-step explanation:
Question (1)
From the table showing arithmetic sequence,
First term of the sequence = 18
5th term of the sequence = -10
Explicit formula of an arithmetic sequence,
[tex]T_{n}=a+(n-1)d[/tex]
For 5th term,
-10 = 18 + (5 -1)d
-10 = 18 + 4d
4d = -28
d = -7
Therefore, explicit formula for the table will be,
[tex]T_n[/tex] = 18 + (n - 1)(-7)
= 18 - 7n + 7
= 25 - 7n
[tex]T_n=25-7n[/tex]
Recursive formula → [tex]T_n=T_{n-1}+d[/tex]
[tex]T_n=T_{n-1}-7[/tex]
Question (2),
From the table attached,
First term of the geometric sequence = 6
5th term = 96
Recursive formula of a geometric sequence = [tex]a(r)^{n-1}[/tex]
Here a = first term
r = common ratio
For 5th term from the table,
96 = [tex]6(r)^{5-1}[/tex]
r⁴ = 16
r = [tex]\sqrt[4]{16}[/tex]
r = 2
Therefore, explicit formula will be,
[tex]T_n=6(2)^{n-1}[/tex]
Recursive formula will be,
[tex]T_n=T_{n-1}\times (r)[/tex]
[tex]T_n=2\times T_{n-1}[/tex]
