Answers

1. A certain sequence has the rule: 3Dn + Dn+1 = Dn+2, and has terms: D5= 45 and D7= 234

A. Find D6=

Start with n=5, so we're using the rule 3D5 + D6 = D7
Plug in the numbers we know to get: 3*45 + D6 = 234
Now solve: 135 + D6 = 234
D6 = 234-135
D6 = 99

B. Find D8=

Start with n=6, so we're using the rule 3D6 + D7 = D8
Plug in the numbers we know to get: 3*99 + 234 = D8
Now solve:

297 + 234 = D8
D8= 531

C. Find D4=

Start with n=4, so we're using the rule 3D4 + D5 = D6
Plug in the numbers we know to get: 3D4 + 45 = 99
Now solve:

3D4= 99 - 45
3D4 = 54
D4= 54/3
D4= 18

D. Find D3=

Start with n=3, so we're using the rule 3D3 + D4 = D5
Plug in the numbers we know to get: 3D3 + 18 = 45
Now solve:

3D3= 45 - 18
3D3 = 27
D3= 27/3
D3= 9

2. A certain sequence has the rule: Dn + 2Dn+1 = Dn+2, and has terms: D6=19 and D8= 111

A. Find D7=

Start with n=6, so we're using the rule D6 + 2D7 = D8
Plug in the numbers we know to get: 19 + 2D7 = 111
Now solve:

2D7 = 111 - 19
2D7 = 92
D7 = 92/2
D7 = 46

B. Find D9=

Start with n=7, so we're using the rule D7 + 2D8 = D9
Plug in the numbers we know to get: 46 + 2*111 = D9
Now solve:

46 + 222 = D9
D9 = 268

C. Find D10=

Start with n=8, so we're using the rule D8 + 2D9 = D10
Plug in the numbers we know to get: 111 + 2*268 = D10
Now solve:

111 + 536 = D10
D10 = 647

D. Find D5

Start with n=5, so we're using the rule D5 + 2D6 = D7
Plug in the numbers we know to get: D5 + 2*19 = 46
Now solve:

D5 + 38 = 46
D5= 46-38
D5 = 8

3. A certain sequence has the rule: 3Dn + 2Dn+1 = Dn+2, and has terms: D5= 42 and D7= 366

A. Find D6=

Start with n=5, so we're using the rule 3D5 + 2D6 = D7
Plug in the numbers we know to get: 3*42 + 2D6 = 366
Now solve:

126 + 2D6 = 366
2D6 = 366 - 126
2D6 = 240
D6 = 240/2
D6 = 120

B. Find D8=

Start with n=6, so we're using the rule 3D6 + 2D7 = D8
Plug in the numbers we know to get: 3*120 + 2*366 =D8
Now solve:

360 + 732 =D8
D8 = 1092

C. Find D4=

Start with n=4, so we're using the rule 3D4 + 2D5 = D6
Plug in the numbers we know to get: 3D4 + 2*42 = 120
Now solve:

3D4 + 84 = 120
3D4= 120 - 84
3D4= 36
D4 = 36/3
D4 = 12

D. Find D3=

Start with n=3, so we're using the rule 3D3 + 2D4 = D5
Plug in the numbers we know to get: 3D3 + 2*12 = 42
Now solve:

3D3 + 24 = 42
3D3= 42 - 24
3D3= 18
D3 = 18/3
D3 = 6