Question 1186523: A student decides to follow a simple scheme to save money. She puts aside 5 peso the first day, 10 pesos the second day, 15 pesos the third day, 20 pesos the fourth day, and so on.
a. Following the pattern of how she saves money, how much will she put aside on the 30th day?
b. How much money will she have at the end of 30 days?
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
A student decides to follow a simple scheme to save money. She puts aside 5 peso the first day,
10 pesos the second day, 15 pesos the third day, 20 pesos the fourth day, and so on.
a. Following the pattern of how she saves money, how much will she put aside on the 30th day?
b. How much money will she have at the end of 30 days?
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(a) Use the formula for the n-th term of an arithmetic progression.
 = 5, d = 5, n= 30.
 = + d*(n-1).
 = 5 + 5*(30-1) = 5 + 5*30 - 5 = 5*30 = 150.
ANSWER. 150 pesos.
(b) Use the formula for the sum of the first n terms of an arithmetic progression.
You know the first term = 5, the last term = 150
and the number of terms n = 30.
So, you can use the simplest formula form
 = 
 =  = use your calculator = 2325.
ANSWER. 2325 pesos.
Solved and explained.
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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.
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