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I tried the problem. The new series follows the formula 7n+1, where n=0, 1, 2,…, 57. So number of terms would be 58.
Is my answer correct?
What about 7n+2,7n+3 and 7n? for example you take mix the sequence 7n+2. then, make sure not including 7n+5 cuz 7n+2+7n+5 will be a multiple of 7. make sure to include only 1 7n(Why? find it yourself). See, also, you can include 7n+5 then you have to exclude 7n+2. see in which case, you get the most amount of number of n’s available(I gave too much hint). I mean, make pairs. mod 1 to mod 6. mod 2 to mod 5. etc. then choose one which you want to include. see in which case, you can increase the amount of n’s.