Answer:
The recursive rule for the sequence is a[tex]_{1}[/tex] = 75; a[tex]_{n}[/tex] = a[tex]_{n-1}[/tex] + 25
Step-by-step explanation:
the recursive rule of an arithmetic function is a[tex]_{1}[/tex] = first term; a[tex]_{n}[/tex]= a[tex]_{n-1}[/tex] + d, where
- a[tex]_{1}[/tex] is the first term
- a[tex]_{n-1}[/tex] is the nth term
- d is the common difference between each 2 consecutive terms
∵ The given is 75, 100, 125, 150, .......
∵ 100 - 75 = 25
∵ 125 - 100 = 25
∵ 150 - 125 = 25
∴ The common difference is 25
∴ d = 25
∵ The first term is 75
∴ a[tex]_{1}[/tex] = 75
→ Substutute the values of a1 and d in the formula above
∴ The recursive rule for the sequence is a[tex]_{1}[/tex] = 75; a[tex]_{n}[/tex] = a[tex]_{n-1}[/tex] + 25
