Answer:
see explanation
Step-by-step explanation:
There is a common difference between the number of push - ups he does each day, that is
19 - 12 = 26 - 19 = 33 - 26 = 7
This indicates the sequence of push- ups is an arithmetic sequence
(b)
A recursive rule allows any term in the sequence to be found by adding the common difference (d) to the previous term.
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d ( n is the term number ) and d = 7 , then
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 7 : a₁ = 12 ← recursive rule
(c)
The nth term ( explicit formula ) for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + d(n - 1)
a₁ is the first term, d the common difference, n the term number
here a₁ = 12, d = 7 , then explicit formula is
[tex]a_{n}[/tex] = 12 + 7(n - 1) = 12 + 7n - 7 = 7n + 5
(c)
substitute n = 20 into the explicit formula
a₂₀ = 7(20) + 5 = 140 + 5 = 145
He should be able to do 145 push- ups on the 20th day.
