The median of a set of consecutive odd intergers is 138. If the greatest integer in the set is 145 what is the smallest integer in the set?

I DONT KNOW :O

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- Oct 29th 2008, 05:10 PMxsrielHave no clue How to do this. neither does dad xD
The median of a set of consecutive odd intergers is 138. If the greatest integer in the set is 145 what is the smallest integer in the set?

I DONT KNOW :O - Oct 29th 2008, 05:16 PMgoomage13
131 perhaps start with 131 go to 145. 138 is the median. i could be wrong, but i think that's right

- Oct 29th 2008, 05:18 PMxsriel
yeah but what does consecutive mean?

- Oct 29th 2008, 05:20 PMxsriel
- Oct 29th 2008, 05:22 PMMathstud28
Consider this...we need a set $\displaystyle \left\{a_1,a_2,\cdots,145\right\}$

Now for the median to 138 we need there to be an even amount of elements the middle two being 139 and 137 so it should be pretty obvious the set is

$\displaystyle \left\{129,\cdots,145\right\}$ - Oct 29th 2008, 05:23 PMMathstud28
- Oct 29th 2008, 05:24 PMeuclid2
- Oct 29th 2008, 05:27 PMxsriel
oh...ill copy down both and ask my teacher xxD but thanks for the help

- Oct 29th 2008, 05:28 PMxsriel
- Oct 29th 2008, 05:28 PMMathstud28
- Oct 29th 2008, 05:31 PMSoroban
Hello, xsriel!

Quote:

The median of a set of consecutive odd integers is 138.

If the greatest integer in the set is 145 what is the smallest integer in the set?

We have__consecutive____odd__integers, like: .$\displaystyle \hdots\;129, 131, 135, 137, 139, 141, 143, 145, 147\; \hdots$

If 138 is the median, it is in the "middle" of the set of integers

. . (with an equal number of integers on both sides).

. . $\displaystyle \begin{array}{cccccccccccc}\hdots & 129 & 131 &133 & 135 & 137 & 139 & 141 & 143 & 145 & 147 & \hdots \end{array}$

. - - . . . . . . . . . . . . . . . . .$\displaystyle \uparrow$

. . . . . . . . . . . . . . . . . . . $\displaystyle 138$

Since the largest number is 145, the sequence looks like this:

. . $\displaystyle \begin{array}{cccccccccccc}131 & 133 & 135 & 137 & 139 & 141 & 143 & 145 \end{array}$

. - . - . . . . . . . . . .$\displaystyle \uparrow$

Therefore, the smallest integer is 131.