Answer :
Final Answer:
a. Arithmetic sequence: 1, 5, 9, 13, ... Next three terms: 17, 21, 25.
b. Arithmetic sequence: 70, 120, 170, ... Next three terms: 220, 270, 320.
c. Geometric sequence: 1, 3, 9, ... Next three terms: 27, 81, 243.
d. Geometric sequence: 10, 10³, 10⁵, 10⁷, ... Next three terms: 10⁹, 10¹¹, 10¹³.
e. Arithmetic sequence: 193 + 7 * 2³⁰, 193 + 8 * 2³⁰, 193 + 9 * 2³⁰, ... Next three terms: 193 + 10 * 2³⁰, 193 + 11 * 2³⁰, 193 + 12 * 2³⁰.
Explanation:
a. The sequence a. is an arithmetic sequence with a common difference of 4. To find the next three terms, we simply add 4 to the last term, so the next terms are 13 + 4 = 17, 17 + 4 = 21, and 21 + 4 = 25.
b. The sequence b. is also an arithmetic sequence with a common difference of 50. To find the next three terms, we add 50 to the last term, so the next terms are 170 + 50 = 220, 220 + 50 = 270, and 270 + 50 = 320.
c. The sequence c. is a geometric sequence with a common ratio of 3. To find the next three terms, we multiply the last term by 3, so the next terms are 9 * 3 = 27, 27 * 3 = 81, and 81 * 3 = 243.
d. The sequence d. is a geometric sequence with a common ratio of 100. To find the next three terms, we multiply the last term by 100, so the next terms are 10⁷ * 100 = 10⁹, 10⁹ * 100 = 10¹¹, and 10¹¹ * 100 = 10¹³.
e. The sequence e. is an arithmetic sequence with a common difference of 2³⁰. To find the next three terms, we add 2³⁰ to the last term, so the next terms are 193 + 13 * 2³⁰, 193 + 14 * 2³⁰, and 193 + 15 * 2³⁰.
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