12-1 Arithmetic Sequences and Series

By: Nina F..- Honors ICM- Blackwell

    At the the small Sanderson Farm  farmers Jill and Buck  live happily. Their animals live according to their ages.  The youngest of all the animals lives closest to the farm house and as the animal's ages increase so does the space between their homes and the farm house.  The farmers just want to make sure the younger animals are okay and adjusting well.  Little Pink is the youngest of the bunch.  He is the one year old piglet that sits closest to the farmer's house.  Next in line are the ponies.  They all are four years old.  After the ponies live the seven year old chickens.  This pattern continues throughout the entire animal living quarters.  At the very end are the old Cows.  They are now forty-nine years old.  Questions:  How many different animal resting quarters are there, and if you were to add up all the different ages of the animals what would the sum of their ages be?

(use your head)

Need Help???

Formula for finding the nth term: 

a_n= a₁+(n-1)d

(a_n=last term, a₁=first term, n=number of terms in the sequence, d=distance between terms)

Step1: Plug the correct numbers in according to the formula.49=1+(n-1)3

Step 2: Distribute the 3.48=3n-3

Step 3: Subtract the 3 from bothe sides of the equation.45=3n

Step 4: Divide both sides of the equation by 3.n=15

There are 15 different animal living quarters on the Sanderson Farm.

Formula for finding the Sum of an Arithmetic Series

S_n=n/2(a₁+a_n)

(S_n= sum of the numbers in the series, a_n=last term, a₁=first term, n=number of terms in the sequence, d=distance between terms)

Step 1: Plug in the correct numbers into the formula. S₅=15/2(1+49)

Step 2: Solve.S₁₅=375

When all the different ages of the animals on the farm are added together you get 375 years.

"Each time you are honest and conduct yourself with honesty, a success force will drive you toward greater success. Each time you lie, even with a little white lie, there are strong forces pushing you toward failure."
-Joseph Sugarman
Quote Provided by:  http://www.quoteland.com

This quotation enphasises the character trait of "honesty."  If you stay honest to yourself and others, you'll feel good about looking in the mirror and the burden of a lie will not be on your shoulders.

All formulas were found in:

• Crosswhite, Joe F.; Gordon-Holliday, Berchie W.; Vannatta, Glen D.; Yunker, Lee E. .Advanced 

                Mathematical Concepts: Precalculus with Applications. New York: Glencoe/McGraw-Hill, 1999.

For more math help on this topic, try:

• www.mathworld.com

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