Answer:
A. [tex]a_n=2a_{n-1}[/tex]
B. 160
Step-by-step explanation:
Silvia does 5 sit-ups on the first day of her exercise program. Each day thereafter she does twice as many sit-ups as the day before. Hence
1st day - 5 sit-ups
2nd day - 10 sit-ups
3rd day - 20 sit-ups
...
A.
[tex]a_1=5\\ \\a_2=2a_1\\ \\a_3=2a_2\\ \\...\\ \\a_n=2a_{n-1}[/tex]
The recursive formula that models the number of sit-ups she does each day is
[tex]a_n=2a_{n-1}[/tex]
B.
[tex]a_6=2a_5=2\cdot 2a_4=4\cdot 2a_3=8\cdot 2a_2=16\cdot 2a_1=32\cdot 5=160[/tex]
Answer:
A.[tex]a_n=2a_{n-1}[/tex]
B.[tex]a_1=5,a_2=10,a_3=20,a_4=40,a_5=80,a_6=160[/tex]
Step-by-step explanation:
We are given that
Silvia does sit-ups on the first day of her exercise program=5
A.we have to find the recursive formula that models the number of sit up she does each day.
According to question
[tex]a_1=5[/tex]
[tex]a_2=2\times 5=2a_1[/tex]
[tex]a_3=2a_2[/tex]
[tex]a_4=2a_3[/tex]
[tex]a_n=2a_{n-1}[/tex]
Hence, the recursive formula is given by
[tex]a_n=2a_{n-1}[/tex]
B.We have to find the number of sit-ups Silvia does on each of the first 6 days by using this formula .
[tex]a_1=5[/tex]
[tex]a_2=2(5)=10[/tex]
[tex]a_3=2(10)=20[/tex]
[tex]a_4=2(20)=40[/tex]
[tex]a_5=2(40)=80[/tex]
[tex]a_6=2(80)=160[/tex]
