In an arithmetic sequence you add or subtract the same numbe each time. In a geometric sequence you multiply or divide by the same number each time. Are the following sequences arithmetic or geometric? a) 5,7,9,11,ldots b) 3,6,12,24,ldots 32, 25, 18, 11, ldots

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Question

In an arithmetic sequence you add or subtract the same numbe each time. In a geometric sequence you multiply or divide by the same number each time. Are the following sequences arithmetic or geometric? a) 5,7,9,11,ldots b) 3,6,12,24,ldots 32, 25, 18, 11, ldots

Answer 1

а) Arithmetic sequence b) Geometric sequence c) Arithmetic sequence

Answer 2

The problem prescribes two different types of series - arithmetic and geometric. Subsequent terms in an arithmetic progression (sequence) can be determined by adding or subtracting a constant difference for each subsequent transition. On the other hand, in a geometric progression the ratio of one term to the previous term is constant and each term can be found either by multiplying it by a constant multiplier or by dividing it by a constant divisor. Part (a): In sequence \( 5, \quad 7, \quad 9, \quad 11, \ldots \), from each term to the next, we're adding 2. This right here is going to be an arithmetic progression where the common difference 'd' equals 2. Part (b): In sequence \( 3,6, \quad 12, \quad 24, \ldots \), each term appears to be 2 times the previous term. The common ratio 'r' in this case is depicted as 2, rendering it a geometric progression. Part (c): Observation of the sequence \( 32, \quad 25, \quad 18, \quad 11, \ldots \) shows the successive terms which is resulting in common difference of negative 7. Our common difference 'd' is -7 for arithmetic sequence, without any multiplication by common factor, thus we have another arithmetic sequence in a descending order catching our attention.

Question

In an arithmetic sequence you add or subtract the same numbe each time. In a geometric sequence you multiply or divide by the same number each time. Are the following sequences arithmetic or geometric? a) 5,7,9,11,ldots b) 3,6,12,24,ldots 32, 25, 18, 11, ldots

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