Henry reads a book with $450$ pages. He reads $2$ pages more than last day he reads. If he finished reading this book in $18$ days, how many pages did Henry read in the first day?
This book has $450$ pages, and he finished reading this book in $18$ days.
Let amount of pages be $x$
$x+2, x+4, x+6, x+8.... $
In 18th day we have
$x+20$
Hence we get
$x+20 = 420$
$x = 21$
Why isn't it correct answer or what am I missing?
Let's say Henry reads x number of pages on the first day. Since every day he reads two pages more than the previous day, he must read $x+2$ on the second day. $x+4$ on third day and so on. There is a pattern there.
On every nth day he reads $ x + 2(n-1) $ pages. On the 18th day he must read $ x + 2(18-1) $ pages.
We are given the book has $450$ pages, that means the sum of all the pages he read every day is equal to $ 450$ $$ x + (x + 2) + (x+4) + ... (x + 34) = 450 $$ $$ 18x + 2 + 4 + 6 ... + 34 = 450 $$ $$ 18x + 2(1+2+3 ... + 17) = 450 $$ $$ 18x + 2\frac{17*18}{2} = 450 $$ $$ 18x + 306 = 450 $$ $$ 18x = 144 $$ $$ x = 8 $$
So Henry read 8 pages on the first day.