Classify the series 12 plus left-parenthesis negative 8 right-parenthesis plus Start Fraction 16 over 3 End Fraction plus left-parenthesis negative Start Fraction 32 over 9 End Fraction right-parenthesis plus Start Fraction 64 over 27 End Fraction plus ellipsis as arithmetic or geometric. Then, determine whether the series is convergent or divergent.
(1 point)
Responses
arithmetic, convergent
arithmetic, convergent
arithmetic, divergent
arithmetic, divergent
geometric, convergent
geometric, convergent
geometric, divergent
geometric, divergent
The given series is an arithmetic series.
To determine if the series is convergent or divergent, we need to examine the common difference between consecutive terms.
The common difference in this series is (-8) - 12 = (-20) / 3 = -6.67.
Since the common difference is not constant and changes with each term, the series is divergent.
Therefore, the correct response is: arithmetic, divergent.