SOLUTION: While on a vacation to the country, a man spent 10 days fishing in the river. On each new, he caught 4 fish more than he had caught the day before. If he caught a total of 200 fish
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Question 1067828: While on a vacation to the country, a man spent 10 days fishing in the river. On each new, he caught 4 fish more than he had caught the day before. If he caught a total of 200 fish how many did he catch on each day?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Do they want an average number of fish caught per day,
do they want the number caught each day as a day-by-day list
or do they want the number caught each day as a function or formula?
This is a case of an arithmetic sequence (or arithmetic progression, as it is called in some places).
Each new day the man catches fish more than he had caught the day before
That means that the number of fish he catches forms an arithmetic sequence (or arithmetic progression).
Some teachers like to see written formulas so you can "show your work,"
but if that is not required, this is a mental math problem,
and you can find the answer quickly an easily,
which is great if you are taking a timed test.
THE FORMULAS
Here is the way I would write them. It is a popular way, but may not be the way your teacher prefers.
= first term of the arithmetic sequence/progression (number of fish caught on day )
= common difference (in this case , because each new day the man catches fish more than he had caught the day before).
= term number
or = sum of the first terms
THE MENTAL MATH:
My telepathic powers are down today,
so I will have to write the mental procedure as equations/formulas.
The nice thing about arithmetic sequences,
is that the average of any number of consecutive terms of such a sequence
is the average of the first and last terms, so
= average number of fish caught per day.
= total number of fish caught in days.
So, we see that the man caught an average of fish per day.
= number of fish caught on day ,
so
We also see that he caught fish the first day:
--> --> .
So, the list of fish caught per day is
The number of fish expressed as a function would be
,
or using an equivalent expression,
.
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