SOLUTION: Is it B? I want to check my answer. James decided to start exercising. The first day he jogged for 10 mins. The next day he wanted to jog for 4 more minutes than the previous da

Question 1161339: Is it B? I want to check my answer.
James decided to start exercising. The first day he jogged for 10 mins. The next day he wanted to jog for 4 more minutes than the previous day. He wanted to continue increasing by the same amount like this for every one of the days in a week.
If he succeeded in doing this how many total minutes did he run for the week?

A. 34 minutes
B. 154 minutes
C. 14 minutes
D. 90 minutes

The question is provided in the link here: https://i.imgur.com/AdSC8Bk.png

Found 4 solutions by MathLover1, MathTherapy, ikleyn, greenestamps:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

yes, it is B
days, each day an increase of min
if first day was, then
second day is, third ,fourth , fifth ,sixt , seventh
so, the sum of all days is

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Is it B? I want to check my answer.
James decided to start exercising. The first day he jogged for 10 mins. The next day he wanted to jog for 4 more minutes than the previous day. He wanted to continue increasing by the same amount like this for every one of the days in a week.
If he succeeded in doing this how many total minutes did he run for the week?

A. 34 minutes
B. 154 minutes
C. 14 minutes
D. 90 minutes

The question is provided in the link here: https://i.imgur.com/AdSC8Bk.png

You're CORRECT, but I do hope you didn't calculate it the way that woman did. That method is extremely inefficient, and very time-consuming.
Somehow I just "feel" that you know that!
Sum of an A.P:

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

            You can solve it differently and even more effectively and less time consuming.

You have an AP with the first term 10; the common difference 4; and the number of therms of 7 (one week). You calculate the 7-th term = = 10 + 6*4 = 34; then you calculate the average of the first and the last terms = = 22; and finally you multiply this average by the number of the terms 7 to get the ANSWER 22*7 = 154 minutes. You can make every step MENTALLY.

Solved.

------------------

For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Tutor @ikleyn shows one efficient way to find the sum, knowing that it is an arithmetic sequence:

(1) use the first term and common difference to find the last (7th) term
(2) find the average of the first and last terms, which is the average of all the terms
(3) multiply that average by the number of terms.

Here is another efficient way....

(1) use the first term and the common difference to find the middle (4th) term, which is the average of all the terms
(2) multiply that average by the number of terms.

middle (4th) term: 10+3(4) = 10+12 = 22
sum: 7(22) = 154

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