Problem Solving

Some sticks have the length from 1/4 to 7/8 inch, inclusive, and from the
shortest to the longest, the length increased by 1/16 inch. What is the median of
these lengths? (All the sticks should different.)
[spoiler]Answer:9/16[/spoiler]
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lcm 16 => lenght 4 to 14; after increasing by 1 from 4 to 15 but 9 isnt median of int. from 9 to 15

what i am doing wrong pls expl.

First off, find the total number of sticks:

1/4+1/16(x)=7/8

x= The total number of sticks increased by 1/16 of an inch that eventually led to the longest stick, whose length was 7/8 of an inch.

x=16(7/8-1/4)=14-4=10

The total number of sticks= 10+1=11 sticks.

We have to add the one to the 10 because we have to include the stick whose length was 1/4 of an inch.

Now, if there were a total of 11 sticks laid out in order from their shortest length to their longest length, then the median length of those sticks would be the 6th stick.

Use the arithmetic progression formula to find out the length of the 6th stick:

an=dn+c

d=difference
c=first term- difference

an=1/16(n)+12/24

a6=1/16(6)+12/24

a6=36/64=9/16