SOLUTION: Subject: locating a number in a triangular array of numbers [Question] if the following number of array continues, where would the number 289 appear?

Question 287195: Subject: locating a number in a triangular array of numbers
[Question]
if the following number of array continues, where would the number 289
appear?
1
3 5
7 9 11
13 15 17 19
21 23 25 27 29
31 33 35 37 39 41
43 45 47 49 51 53 55
57 59 61 63 65 67 69 71

[Difficulty]
I am able to calculate that 289 is the 145th term in the sequence,
using the arithmetic formular below (on the next section below)
But my problem is that how do you locate, the number (289) in terms of
ROWS. I can see that there are 8 rows. in other words i would like to
know how do you assign the row number for 289 (145th term) ?. is
there any sort of formular for finding the row number in the
triangular array of these numberS.
[Thoughts]
Okay, i can see that its an arithmetic sequence of odd number with
d=2. In locating the number in the triangular array, i have to look
for n, i know that a1=1 and so for 289 An = 289 , the using the formular:
an = a1 + (n-1)d
289 = 1 + (n-1)2
288 = (n-1)2
n = 145
So, that means that 289 is the 145th term in the sequence.

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the number of terms in a row is the same as the number of the row

so the cumulative number of terms through row "r" is ___ n = (r+1)(r/2) = (r^2 + r) / 2

290 = r^2 + r ___ 0 = r^2 + r - 290

use the quadratic formula to find r ___ then round up to the next integer
___ this should be the row containing 289

find n for the preceding row, and you will know the position of 289 in the row
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