Question

the first four terms of a sequence are given. can these terms be the terms of an arithmetic sequence?ln(2), ln(4), ln(8), ln(16),yes, the sequence is arithmetic.no, the sequence is not arithmetic.

Answer 1

Yes, it's an arithmetic sequence with a common difference of ln(2) between consecutive terms.

ln(4) - ln(2) = ln(2²) - ln(2) = 2 ln(2) - ln(2) = ln(2)

ln(8) - ln(4) = ln(2³) - ln(2²) = 3 ln(2) - 2 ln(2) = ln(2)

ln(16) - ln(8) = ln(2⁴) - ln(2³) = 4 ln(2) - 3 ln(2) = ln(2)