determine the common difference, and find the next four terms of each arithmetic sequence.
1. $20, 17, 14, \dots$
2. $3, 16, 29, \dots$
3. $117, 108, 99, \dots$
4. $-83, -61, -39, \dots$
5. $-3, 1, 5, \dots$
6. $4, 21, 38, \dots$
7. $-4.5, -9.5, -14.5, \dots$
8. $-97, -29, 39, \dots$

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{ "quality": "clear", "question_count": 8, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Sequences" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequences" ] } ## Calculate common differences $$ \begin{aligned} d_1 &= 17 - 20 = -3 \ d_2 &= 16 - 3 = 13 \ d_3 &= 108 - 117 = -9 \ d_4 &= -61 - (-83) = 22 \ d_5 &= 1 - (-3) = 4 \ d_6 &= 21 - 4 = 17 \ d_7 &= -9.5 - (-4.5) = -5 \ d_8 &= -29 - (-97) = 68 \end{aligned} $$ ## Generate next four terms $$ \begin{aligned} \text{Seq 1: } & 14 + (-3) = 11,\ 11 + (-3) = 8,\ 8 + (-3) = 5,\ 5 + (-3) = 2 \ \text{Seq 2: } & 29 + 13 = 42,\ 42 + 13 = 55,\ 55 + 13 = 68,\ 68 + 13 = 81 \ \text{Seq 3: } & 99 + (-9) = 90,\ 90 + (-9) = 81,\ 81 + (-9) = 72,\ 72 + (-9) = 63 \ \text{Seq 4: } & -39 + 22 = -17,\ -17 + 22 = 5,\ 5 + 22 = 27,\ 27 + 22 = 49 \ \text{Seq 5: } & 5 + 4 = 9,\ 9 + 4 = 13,\ 13 + 4 = 17,\ 17 + 4 = 21 \ \text{Seq 6: } & 38 + 17 = 55,\ 55 + 17 = 72,\ 72 + 17 = 89,\ 89 + 17 = 106 \ \text{Seq 7: } & -14.5 + (-5) = -19.5,\ -19.5 + (-5) = -24.5,\ -24.5 + (-5) = -29.5,\ -29.5 + (-5) = -34.5 \ \text{Seq 8: } & 39 + 68 = 107,\ 107 + 68 = 175,\ 175 + 68 = 243,\ 243 + 68 = 311 \end{aligned} $$ | No. | Common Difference | Next Four Terms | |---|---|---| | 1 | $d = -3$ | $11, 8, 5, 2$ | | 2 | $d = 13$ | $42, 55, 68, 81$ | | 3 | $d = -9$ | $90, 81, 72, 63$ | | 4 | $d = 22$ | $-17, 5, 27, 49$ | | 5 | $d = 4$ | $9, 13, 17, 21$ | | 6 | $d = 17$ | $55, 72, 89, 106$ | | 7 | $d = -5$ | $-19.5, -24.5, -29.5, -34.5$ | | 8 | $d = 68$ | $107, 175, 243, 311$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Arithmetic Sequences" ] }

No.	Common Difference	Next Four Terms
2	\(d = 13\)	\(42, 55, 68, 81\)
3	\(d = -9\)	\(90, 81, 72, 63\)
4	\(d = 22\)	\(-17, 5, 27, 49\)
5	\(d = 4\)	\(9, 13, 17, 21\)
6	\(d = 17\)	\(55, 72, 89, 106\)
7	\(d = -5\)	\(-19.5, -24.5, -29.5, -34.5\)
8	\(d = 68\)	\(107, 175, 243, 311\)

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