Question

An = 3.5 +2.8 (n-1)
f(n) =

Answer 1

f(n) = 2.8n + 0.7

Explanation:

The form of the linear function is f(x) = m x + b, where

• x is the input

• f(x) is the output

Let us solve the question

∵ The rule of the arithmetic sequence is a
`_(n)` = 3.5 + 2.8(n - 1), where

• a
  `_(n)` is the nth term ⇒ output

• n is the number of the term ⇒ input

→ To write it as a function replace a
`_(n)` by f(n)

∵ a
`_(n)` = f(n)

∴ f(n) = 3.5 + 2.8(n - 1)

→ Simplify the right side to make it in the form of the function above

∵ f(n) = 3.5 + 2.8(n) + 2.8(-1)

→ Remember (+)(-) = (-)

∴ f(n) = 3.5 + 2.8n - 2.8

→ Add the like terms in the right side

∵ f(n) = 2.8n + (3.5 - 2.8)

∴ f(n) = 2.8n + 0.7