document.write( "Question 287195: Subject: locating a number in a triangular array of numbers \r
\n" ); document.write( "\n" ); document.write( "[Question]
\n" ); document.write( "if the following number of array continues, where would the number 289
\n" ); document.write( "appear?
\n" ); document.write( " 1
\n" ); document.write( " 3 5
\n" ); document.write( " 7 9 11
\n" ); document.write( " 13 15 17 19
\n" ); document.write( " 21 23 25 27 29
\n" ); document.write( " 31 33 35 37 39 41
\n" ); document.write( " 43 45 47 49 51 53 55
\n" ); document.write( " 57 59 61 63 65 67 69 71
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "[Difficulty]
\n" ); document.write( "I am able to calculate that 289 is the 145th term in the sequence,
\n" ); document.write( "using the arithmetic formular below (on the next section below)
\n" ); document.write( "But my problem is that how do you locate, the number (289) in terms of
\n" ); document.write( "ROWS. I can see that there are 8 rows. in other words i would like to
\n" ); document.write( "know how do you assign the row number for 289 (145th term) ?. is
\n" ); document.write( "there any sort of formular for finding the row number in the
\n" ); document.write( "triangular array of these numberS.\r
\n" ); document.write( "\n" ); document.write( "[Thoughts]
\n" ); document.write( "Okay, i can see that its an arithmetic sequence of odd number with
\n" ); document.write( "d=2. In locating the number in the triangular array, i have to look
\n" ); document.write( "for n, i know that a1=1 and so for 289 An = 289 , the using the formular:
\n" ); document.write( " an = a1 + (n-1)d
\n" ); document.write( " 289 = 1 + (n-1)2
\n" ); document.write( " 288 = (n-1)2
\n" ); document.write( " n = 145
\n" ); document.write( "So, that means that 289 is the 145th term in the sequence.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #208342 by scott8148(6628) $\"\"$ $\"About$

You can put this solution on YOUR website!
the number of terms in a row is the same as the number of the row\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so the cumulative number of terms through row \"r\" is ___ n = (r+1)(r/2) = (r^2 + r) / 2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "290 = r^2 + r ___ 0 = r^2 + r - 290\r
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\n" ); document.write( "\n" ); document.write( "use the quadratic formula to find r ___ then round up to the next integer
\n" ); document.write( "___ this should be the row containing 289\r
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\n" ); document.write( "\n" ); document.write( "find n for the preceding row, and you will know the position of 289 in the row \n" ); document.write( "

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