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The arithmetic progressions 2, 5, 8, 11 ... and 3, 10, 17, 24 ... have some common values. What is the largest value less than 500 that they have in common?

 Aug 10, 2018
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2 + (m - 1)*3 =3 + (n -1)*7, solve for m, n

3 m + 3 = 7 n

m =160 and n =69

2 + (160 -1)*3 =479 - the 160th term in the first AP

3 + (69 - 1)*7  =479 - the 69th term in the second AP.

Note: The terms are both LESS  than 500. However, 500 itself is shared between the two APs.

 Aug 10, 2018
edited by Guest  Aug 10, 2018
edited by Guest  Aug 10, 2018

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