According to: http://www.phrases.org.uk/bulletin_board/17/messages/380.html
The term five by five refers to the two measures of signal strength and readability; it is derived from older HAM radio instruments that were scaled from zero to 10 with 10 being the strongest. A five by five would be interpreted as 50 percent signal strength and easily readable, perhaps with some static or band clutter. A 10 by two would have a strong signal, but be broken and hard to understand, while a two by 10 would contain a weak signal, but be perfectly clear. A 10 by 10 would be very strong and crystal clear.
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Factor out each term by term to get: 5 x 7007 = 5 x 7 x 1001 = 5 x 7 x 13 x 77 = 5 x 7² x 11 x 13
It is an arithmetic series with initial number as 7 and an increment of -5, hence the nth term in general = (7 - 5 x n). You can verify this 0th term = (7 - 5 x 0) = 7 1st term = (7 - 5 x 1) = 2 2nd term = (7 - 5 x 2) = -3 ... ... 14th term = (7 - 5 x 14) = -63
675/975 = 135 x 5/195 x 5 = 27 x 5/39 x 5 = 9 x 3/13 x 3 = 9/13
Each term is increased by adding five times three to an increasing exponent. 2 + 5 x 3 to the zero = 7 + 5 x 3 to the first = 22 + 5 x 3 squared = 67 The next term would be 202 which makes the rule something like n = n + 5 x 3 to the x+1, but please double-check that.
Each term in the sequence is three times the previous term plus two, so the next term is 485.1 (3 x 1 + 2) 5 (3 x 5 + 2) 17 (3 x 17 + 2) 53 (3 x 53 = 2) 161 (3 x 161 + 2) 485