Question

If f(1) =12 and f(n)= f(n-1) - 4 then which of the following represents the value of f (40)

Answer 1

Solve It for an arithmetic sequence

• First term=a=12
• Common difference=d=-4

So

• a_n=a+(n-1)d

Hence

a_40:-

• a+(40-1)d
• a+39d
• 12+39(-4)
• 12-156
• -144

Answer 2

`f(40)=-144`

Explanation:

Given:

• 
  `f(1)=12`
• 
  `f(n)=f(n-1)-4`

This is a recursive arithmetic sequence since each term is defined using the previous term.

To find the nth term, convert the recursive formula to an explicit formula.

Explicit form of an arithmetic sequence:
`a_n=a+(n-1)d`

where:

• 
  `a_n` is the nth term
• a is the first term
• d is the common difference between terms

We have been given the first term:
`a=12`

To get any term from its previous term we subtract 4, so the common different (d) is -4.

Therefore, the formula for the nth term is:

`\implies a_n=12+(n-1)(-4)`

`\implies f(n)=16-4n`

To find
`f(40)` simply substitute n = 40 into the explicit formula:

`\implies f(40)=16-4(40)=-144`