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# arithmetic progression

Can anyone have a solution about how to find common elements in two arithmetic progressions?? E.g. First seq is 2,17,32,47,.... Second seq is 67,147,227,... First common term is 227. So how to find these common terms in any given sequences?

Note by Milind Joshi
2 years, 9 months ago

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Find the n'th term of both the Progressions and equate them as follows:

Let the NUMBER of term which is same is 'n' in the first sequence and 'N' in the second sequence. Therefore, since it is same in both the sequences,

                                            2 + (n-1)*15  =  67 + (N-1)*80
= > 2 + 15n - 15  =  67 + 80N - 80
=>  15n - 13 = 80N - 13
=>  3n = 16N


Since, we need to find the first common term, so the values of n and N for which it is true is 16 and 3 respectively. Therefore, n = 16...Putting it in 2 + (n-1)*15, we get the common term as 227...Volaa!!!! · 2 years, 9 months ago