Zina spends 1.5 hours setting up her sewing machine and making one hat. The total amount of time spent making hats can be represented by the sequence below.
1.5, 2.25, 3.0, 3.75, ...
Which recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously?
f(n + 1) = f(n) + 1.5
f(n + 1) = f(n) + 0.75
f(n + 1) = one-halff(n)
f(n + 1) = three-halvesf(n)
Answers
Answer:
Let
\begin{gathered} f(1)=1.5\\ f(2)=2.25\\ f(3)=3\\ f(4)=3.75 \end{gathered}
f(1)=1.5
f(2)=2.25
f(3)=3
f(4)=3.75
we know that
\begin{gathered} f(2)-f(1)=2.25-1.5=0.75\\ f(2)=f(1)+0.75\\ \\ f(3)-f(2)=3-2.25=0.75\\ f(3)=f(2)+0.75\\ \\ f(4)-f(3)=3.75-3=0.75\\ f(4)=f(3)+0.75\\ \\.\\.\\.\\ f(n+1)=f(n)+0.75 \end{gathered}
f(2)−f(1)=2.25−1.5=0.75
f(2)=f(1)+0.75
f(3)−f(2)=3−2.25=0.75
f(3)=f(2)+0.75
f(4)−f(3)=3.75−3=0.75
f(4)=f(3)+0.75
.
.
.
f(n+1)=f(n)+0.75
This is an arithmetic sequence, the common difference is equal to 0.750.75
therefore
the answer is the option
B. f(n + 1) = f(n) + 0.75
Answer:
f( n + 1 ) = f( n ) + 0.75
Step-by-step explanation:
Given :- The given sequence is 1.5, 2.25, 3.0, 3.75, 4.5, 5.25, 6.0, .......
To Find :- The recursive formula used to determine the total amount of time spent making hats based on the total amount of time spent previously.
Solution :-
The given AP sequence is
1.5, 2.25, 3.0, 3.75, 4.5, 5.25, 6.0, .......
First term = 1.5
Common difference = 2nd term - 1st term
= 2.25 - 1.5
= 0.75
So, f( n + 1 ) = f( n ) + 0.75
For n = 1, f( 2 ) = f( 1 ) + 0.75
⇒ 2.25 = 1.5 + 0.75
Therefore, the recursive formula used to determine the total amount of time spent making hats based on the total amount of time spent previously is f( n + 1 ) = f( n ) + 0.75 .
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