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When reading book, Charlie made a list by writing down the page number of the last page he finished reading at the end of each day. (He always finished reading a page he started.) His mom thought his list indicated the amount of pages he had read on each day. At the end of the 8th day of reading, she added the numbers on his list and thought Charlie had read 432 pages. If Charlie started reading the book on page one, and he read the same amount of pages each day of this eight-day period, how many pages did he actually read by the end of the 8th day?

 Jul 25, 2019
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\(p_n = a\cdot n\\ \sum \limits_{n=1}^8p_n=432\\ a\sum \limits_{n=1}^8 n = 432\\ a \dfrac{8(8+1)}{2} = 432\\ 36a=432\\ a=12\\ 8\cdot 12 = 96~\text{pages}\)

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 Jul 25, 2019

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