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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?

  • Precalculas -

    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

    10+29*11 = 329

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

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