The sum of the first 30 terms of one arithmetic sequence is 300 more than the sum of the first 30 terms of another arithmetic sequence. what could the sequences be?

Answer 1

assume they have the same first term.
Then 29(d2-d1) = 300

29 does not divide 300, but it does divide 290

So, in order for s2=s1+300, a2-a1=10

one solution would be

a1=0 d1=1
a2=10 d2=11

0+29=29
10+29*11 = 329

a1+29d1 + 300 = (a1+10) + 29(d1+10)