Question

going up, going down
match each description below with a partially completed number sequence. then complete the sequence.

1. increase by 1 c 6, 7, 8, -9, -10, -11
2. decrease by 1 a 6, 4, 2, 0, 2, 4
3. increase by 2 b -3, 2, 1, 0, 1, 2
4. decrease by 2 d 10, 12, 14, -16, -18, -19
5. increase by 3 f 2, -1, -4, -7, -10, -13
6. decrease by 3 e 2, 1, 4, 7, 10, 13
7. increase by 4 j -3, 2, 7, 12, 17, 22
8. decrease by 4 h 3, -1, -5, -9, -13, -17
9. increase by 5 g -4, 2, 8, 14, 20, 26
10. decrease by 5 k -10, -6, 2, 2, 6, 10
11. increase by 6 i 4, -1, -6, -11, -16, -21
12. decrease by 6 n 6, -5, -7, -6, -8, -7
13. increase by 1, decrease by 2 l -8, -6, -7, -6, -5, -4
14. increase by 2, decrease by 1 m 2, -4, -10, -16, -22, -28
15. make your own pattern including the integers -12, 12, -4, 4, and 0. describe your pattern.

Explanation:

Step1: Verify matches & complete sequences

1. Increase by 1 (C): $6,7,8,\boldsymbol{9},\boldsymbol{10},\boldsymbol{11}$ (add 1 each)
2. Decrease by 1 (A): $6,4,2,\boldsymbol{0},\boldsymbol{-2},\boldsymbol{-4}$ (subtract 2 each? Correction: original sequence follows decrease by 2, correct match for decrease by 1 is sequence with values decreasing by 1: e.g., $8,7,6,\boldsymbol{5},\boldsymbol{4},\boldsymbol{3}$ but given paper's marked A: $6,4,2,0,-2,-4$ is decrease by 2, so correction:

• Decrease by 1: sequence with values reducing by 1, e.g., $9,8,7,\boldsymbol{6},\boldsymbol{5},\boldsymbol{4}$

1. Increase by 2 (B): $-3,-2,-1,\boldsymbol{0},\boldsymbol{1},\boldsymbol{2}$ (add 1 each? Correction: correct increase by 2: $-3,-1,1,\boldsymbol{3},\boldsymbol{5},\boldsymbol{7}$; paper's B is increase by 1)
2. Decrease by 2 (D): $10,12,14,\boldsymbol{16},\boldsymbol{18},\boldsymbol{20}$ (add 2 each? Correction: correct decrease by 2: $10,8,6,\boldsymbol{4},\boldsymbol{2},\boldsymbol{0}$; paper's D is increase by 2)
3. Increase by 3 (F): $2,-1,-4,\boldsymbol{-7},\boldsymbol{-10},\boldsymbol{-13}$ (subtract 3 each? Correction: correct increase by 3: $2,5,8,\boldsymbol{11},\boldsymbol{14},\boldsymbol{17}$; paper's F is decrease by 3)
4. Decrease by 3 (E): $2,1,4,\boldsymbol{7},\boldsymbol{10},\boldsymbol{13}$ (add 3 each? Correction: correct decrease by 3: $7,4,1,\boldsymbol{-2},\boldsymbol{-5},\boldsymbol{-8}$; paper's E is increase by 3)
5. Increase by 4 (J): $-3,2,7,\boldsymbol{12},\boldsymbol{17},\boldsymbol{22}$ (add 5 each? Correction: correct increase by 4: $-3,1,5,\boldsymbol{9},\boldsymbol{13},\boldsymbol{17}$; paper's J is increase by 5)
6. Decrease by 4 (H): $3,-1,-5,\boldsymbol{-9},\boldsymbol{-13},\boldsymbol{-17}$ (subtract 4 each: correct)
7. Increase by 5 (G): $-4,2,8,\boldsymbol{14},\boldsymbol{20},\boldsymbol{26}$ (add 6 each? Correction: correct increase by 5: $-4,1,6,\boldsymbol{11},\boldsymbol{16},\boldsymbol{21}$; paper's G is increase by 6)
8. Decrease by 5 (K): $-10,-6,-2,\boldsymbol{2},\boldsymbol{6},\boldsymbol{10}$ (add 4 each? Correction: correct decrease by 5: $10,5,0,\boldsymbol{-5},\boldsymbol{-10},\boldsymbol{-15}$; paper's K is increase by 4)
9. Increase by 6 (I): $4,-1,-6,\boldsymbol{-11},\boldsymbol{-16},\boldsymbol{-21}$ (subtract 5 each? Correction: correct increase by 6: $4,10,16,\boldsymbol{22},\boldsymbol{28},\boldsymbol{34}$; paper's I is decrease by 5)
10. Decrease by 6 (N): $6,-5,-7,\boldsymbol{-6},\boldsymbol{-8},\boldsymbol{-7}$ (alternate ±1? Correction: correct decrease by 6: $12,6,0,\boldsymbol{-6},\boldsymbol{-12},\boldsymbol{-18}$; paper's N is increase by 1, decrease by 2)
11. Increase by 1, decrease by 2 (L): $-8,-6,-7,\boldsymbol{-6},\boldsymbol{-5},\boldsymbol{-4}$ (alternate +2,-1? Correction: correct pattern: start at $-12$, +1→$-11$, -2→$-13$, +1→$-12$, -2→$-14$)
12. Increase by 2, decrease by 1 (M): $2,-4,-10,\boldsymbol{-16},\boldsymbol{-22},\boldsymbol{-28}$ (subtract 6 each? Correction: correct pattern: start at $0$, +2→$2$, -1→$1$, +2→$3$, -1→$2$)

Step2: Create custom pattern (Q15)

Design a pattern using $-12,12,-4,4,0$: alternate between adding 8 and subtracting 16, or use a symmetric pattern:
Start at $-12$, add 8→$-4$, add 8→$4$, subtract 4→$0$, add 12→$12$, subtract 24→$-12$

Answer:

Corrected Matches & Sequences:

1. Increase by 1: $6,7,8,9,10,11$
2. Decrease by 1: $9,8,7,6,5,4$
3. Increase by 2: $-3,-1,1,3,5,7$
4. Decrease by 2: $10,8,6,4,2,0$
5. Increase by 3: $2,5,8,11,14,17$
6. Decrease by 3: $7,4,1,-2,-5,-8$
7. Increase by 4: $-3,1,5,9,13,17$
8. Decrease by 4: $3,-1,-5,-9,-13,-17$ (correct)
9. Increase by 5: $-4,1,6,11,16,21$
10. Decrease by 5: $10,5,0,-5,-10,-15$
11. Increase by 6: $4,10,16,22,28,34$
12. Decrease by 6: $12,6,0,-6,-12,-18$
13. Increase by 1, decrease by 2: $-12,-11,-13,-12,-14,-13$
14. Increase by 2, decrease by 1: $0,2,1,3,2,4$
15. Custom pattern: $-12, -4, 4, 0, 12, -12$

Pattern description: Start at $-12$, add 8 to get the next term, add 8 again, subtract 4, add 12, then subtract 24 to loop back to the starting value. This pattern includes all required integers: $-12, 12, -4, 4, 0$.