Question

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

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.

(A)Write a recursive formula that models the number of sit-ups she does each day.
(B)Use your formula to find the number of sit-ups Silvia does on each of the first 6 days.

Answer 1

A.
`a_n=2a_(n-1)`

B. 160

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

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`

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* 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`