Question

This question has two parts. First answer Part A, then answer Part B. Part A

Answer 1

Answer:

A. $a_n=2a_{n-1}$

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.

$a_1=5\\ \\a_2=2a_1\\ \\a_3=2a_2\\ \\...\\ \\a_n=2a_{n-1}$

The recursive formula that models the number of sit-ups she does each day is

$a_n=2a_{n-1}$

B.

$a_6=2a_5=2\cdot 2a_4=4\cdot 2a_3=8\cdot 2a_2=16\cdot 2a_1=32\cdot 5=160$

Answer 2

Answer:

A.$a_n=2a_{n-1}$

B.$a_1=5,a_2=10,a_3=20,a_4=40,a_5=80,a_6=160$

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

$a_1=5$

$a_2=2\times 5=2a_1$

$a_3=2a_2$

$a_4=2a_3$

$a_n=2a_{n-1}$

Hence, the recursive formula is given by

$a_n=2a_{n-1}$

B.We have to find the number of sit-ups Silvia  does on each of the first 6 days by using this formula .

$a_1=5$

$a_2=2(5)=10$

$a_3=2(10)=20$

$a_4=2(20)=40$

$a_5=2(40)=80$

$a_6=2(80)=160$