please help dont understand

Question

Jerry started doing sit-ups every day. The first day he did 15 sit-ups. Every day after that he did 2 more sit-ups than he had done the previous day. Today Jerry did 33 sit-ups. Write an equation that could be solved to find the number of days Jerry has been doing sit-ups, not counting the first day.



THANK YOU!

Answer 1

Consider the information you are given. Jerry does 15 sit-ups on the first day, 17 on the second, 19 on the third, etc. In general, if x is the number of days he has been doing sit-ups, the number of sit-ups he does on day x can be expressed as Sit-Ups = 15 + 2*(x-1). Look at what the equation says. On the first day (x=1),

Sit-Ups = 15 + 2*(1-1) = 15 + 2*(0) =15. On the second day (x=2), Sit-Ups = 15 + 2*(2-1) = 15+ 2*(1) = 15+2=17. As x goes up, Sit-Ups adds two each day, exactly as per the statement of the problem.

Now, to determine the number of days Jerry has been doing sit-ups, rearrange the problem to solve for x.

Subtract 15 from both sides to get

Sit-Ups -15 = 2*(x-1)

Divide both sides by 2 to get

(Sit-Ups - 15)/2 = x-1

Add one to each side to get

[ (Sit-Ups -15)/2 ] +1 = x

However, this is the number of days INCLUDING the first day. You are asked to find the number of days EXCLUDING the first day, so subtract one from the left hand side to get the final answer

Number of days (excluding first day) = (Sit-Ups -15)/2

Answer 2

Jerry started doing sit-ups every day. The first day he did 15 sit-ups. Every day after that he did 2 more sit-ups than he had done the previous day. Today Jerry did 33 sit-ups. Write an equation that could be solved to find the number of days Jerry has been doing sit-ups, not counting the first day.



=>

let no. of days = n

15 + 2(n-1) = 33

so on first day= 15 +2(1-1)=15

on second day = 15+2(2-1)=17

on third day = 15+2(3-1)=19 like this

Answer 3

This is considered an arithmetic sequence since we are adding to the number of sit ups he is doing. The formula we will use is:

a_n=a₁+d(n-1)

N is the number of days (this is what we are solving for)

a_n is the number of sit ups he has done on “n” days (33)

a₁ is the number of sit ups he did on the first day (15)

d is the number of sit ups he adds each day (2)

now we just plug everything in:

33 = 15 + 2(n-1)

now we can solve:

33 = 15 + 2n - 2

33 = 13 + 2n

-13. -13

20 = 2n

/2. /2

10 days = n

the problem indicates we shouldn’t include the first day he did sit ups so just subtract one from our final answer. So he has been doing sit ups for 9 days total not including the first day.

there you go! If you have questions don’t hesitate to reach out