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------------------------------------------------ Each of the following sequences is either arithmetic or geometric. Identify the sequences and list the next three terms for each.

a. 1, 5, 9, 13, . . .

b. 70, 120, 170, . . .

c. 1, 3, 9, . . .

d. 10, 10^3, 10^5, 10^7, . . .

e. 193 + 7 \cdot 2^{30}, 193 + 8 \cdot 2^{30}, 193 + 9 \cdot 2^{30}, . . .

Identifying and listing the next three terms for each given sequence: arithmetic sequence a and b, geometric sequence c and d, and arithmetic sequence e.

Explanation:

a. Arithmetic Sequence

The common difference in this sequence is 4, so we add 4 to each term to get the next three terms: 17, 21, 25.

b. Arithmetic Sequence

The common difference in this sequence is 50, so we add 50 to each term to get the next three terms: 220, 270, 320.

c. Geometric Sequence

The common ratio in this sequence is 3, so we multiply each term by 3 to get the next three terms: 27, 81, 243.

d. Geometric Sequence

The common ratio in this sequence is 1000, so we multiply each term by 1000 to get the next three terms: 10^9, 10^11, 10^13.

e. Arithmetic Sequence

The common difference in this sequence is 2^30, so we add 2^30 to each term to get the next three terms: 193 + 10 * 2^30, 193 + 11 * 2^30, 193 + 12 * 2^30.

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