Answer:
34 + 8n
Step-by-step explanation:
a₁ = 42
[tex]a_{n} = a_{n-1} + 8[/tex]
a₂ = a₁ + 8 = 42 + 8 = 50
a₃ = a₂ + 8 = 50 + 8 = 58
a₄ = a₃ + 8 = 58 + 8 = 66
Arithmetic sequence: 42, 50 , 58 , 66, ......
a₁ = 42 ; d = 8
[tex]a_{n}[/tex] = a₁ + d(n-1)
= 42 + 8(n - 1)
= 42 + 8n - 8
= 34 + 8n
Answer:
[tex]a_{n}[/tex] = 8n + 34
Step-by-step explanation:
The explicit rule for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given the recursive rule
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 8
where + 8 is the common difference d , then
[tex]a_{n}[/tex] = 42 + 8(n - 1) = 42 + 8n - 8 = 8n + 34
Explicit rule is
[tex]a_{n}[/tex] = 8n + 34
