Laura C.
Honors ICM 2nd period
Chapter 12.2
Geometric Sequences and Series
Grace is going on a senior class trip with her high school to Disney World. Her parents gave her just enough money to buy food for herself and souvenirs for her family. She spent $2.50 on the first gift, which was a key chain for her little sister. It just so happened that for the rest of the time she spent money, she spent 2 times as much as the time before. Overall, Grace bought 8 items. What is the sum total she spent in all? Also, find how much the last item, a watercolor painting for her mother, cost.
~To answer the first part, finding the sum, use the formula S= a1(1-rn)/(1-r). r can not be = to 1.
~We are looking for S, the sum total of money grace spent.
*A1, being the first term, is given to us, it is 2.50.
*r is the ratio, or order of the pattern. We learned r is 2 because every time she spent 2 times as much as the time before.
*n is the number of terms and we know she bought 8 items, thus n=8.
~Now, we are to plug the known numbers into the formula given above. S= 2.50(1-28)/1-2 Solve this!!
S= $637.50 Grace spent a total of $637.50 in Disney World!!!
~Now we will solve the second part of the world problem.:)
~We are to find the cost of the last item Grace bought which was the watercolor painting for her mother.
There is a formula for this also!!!
L=arn-1
*****HINT******** Although we are solving for a different term in this part of the problem, we can use the same terms given in the word problem in each formula we use!!
*L is what we are looking for, it stands for the last term.
*a is again the first term, which is 2.50.
*r is again the ratio or order of the pattern. r=2.
*n is the numbers of terms, n=8.
~Now plug these numbers into the equation given above.
L=2.50(2)8-1
L=320 Grace spent $320 on the watercolor painting for her mother, which was the last item she bought!!!
"When you get to the end of your rope, tie a knot and hang on." -Franklin D. Roosevelt
This quote is a prime example of perseverance. To persevere is to keep going and not give up on something no matter how difficult, scary or boring it may be. Continue until your task is finished and do not give up on the way.
This quote displays perseverance because even when one gets to the end of their patience or gets discouraged and wants to give up, they must keep going and not give up until the task is finished. In the end, it will work out for the best, as long as they do not give up!!