Question

What's the recursive rule for this sequence? 75, 100, 125, 156,

Answer 1

The recursive rule for the sequence is a
`_(1)` = 75; a
`_(n)` = a
`_(n-1)` + 25

Explanation:

the recursive rule of an arithmetic function is a
`_(1)` = first term; a
`_(n)`= a
`_(n-1)` + d, where

• a
  `_(1)` is the first term

• a
  `_(n-1)` 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
`_(1)` = 75

→ Substutute the values of a1 and d in the formula above

∴ The recursive rule for the sequence is a
`_(1)` = 75; a
`_(n)` = a
`_(n-1)` + 25