Full unit practice requiring complete reasoning and representation checks.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u10-l01', 'number': 1, 'title': 'Sequences, Recursive Definitions & Explicit Rules', 'family': 'sequences', 'week': 29, 'unit': 10, 'unit_title': 'Sequences, Series & Discrete Growth', 'essential': 'How do recursive and explicit structures describe discrete change, accumulation, convergence, and financial or scientific processes?', 'project': 'Discrete Growth, Finance & Convergence Investigation'}
Find the next term: 4,9,14,19,…
2. {'id': 'u10-l01', 'number': 1, 'title': 'Sequences, Recursive Definitions & Explicit Rules', 'family': 'sequences', 'week': 29, 'unit': 10, 'unit_title': 'Sequences, Series & Discrete Growth', 'essential': 'How do recursive and explicit structures describe discrete change, accumulation, convergence, and financial or scientific processes?', 'project': 'Discrete Growth, Finance & Convergence Investigation'}
Write an explicit rule for 4,9,14,…
3. {'id': 'u10-l01', 'number': 1, 'title': 'Sequences, Recursive Definitions & Explicit Rules', 'family': 'sequences', 'week': 29, 'unit': 10, 'unit_title': 'Sequences, Series & Discrete Growth', 'essential': 'How do recursive and explicit structures describe discrete change, accumulation, convergence, and financial or scientific processes?', 'project': 'Discrete Growth, Finance & Convergence Investigation'}
Find a_8 for a_n=3·2^{n−1}.
4. {'id': 'u10-l01', 'number': 1, 'title': 'Sequences, Recursive Definitions & Explicit Rules', 'family': 'sequences', 'week': 29, 'unit': 10, 'unit_title': 'Sequences, Series & Discrete Growth', 'essential': 'How do recursive and explicit structures describe discrete change, accumulation, convergence, and financial or scientific processes?', 'project': 'Discrete Growth, Finance & Convergence Investigation'}
Give a recursive rule for 10,7,4,1,…
5. {'id': 'u10-l01', 'number': 1, 'title': 'Sequences, Recursive Definitions & Explicit Rules', 'family': 'sequences', 'week': 29, 'unit': 10, 'unit_title': 'Sequences, Series & Discrete Growth', 'essential': 'How do recursive and explicit structures describe discrete change, accumulation, convergence, and financial or scientific processes?', 'project': 'Discrete Growth, Finance & Convergence Investigation'}
Is 2,6,18,54 arithmetic or geometric?
6. {'id': 'u10-l01', 'number': 1, 'title': 'Sequences, Recursive Definitions & Explicit Rules', 'family': 'sequences', 'week': 29, 'unit': 10, 'unit_title': 'Sequences, Series & Discrete Growth', 'essential': 'How do recursive and explicit structures describe discrete change, accumulation, convergence, and financial or scientific processes?', 'project': 'Discrete Growth, Finance & Convergence Investigation'}
Find the 20th term of a_n=7+4(n−1).
7. {'id': 'u10-l02', 'number': 2, 'title': 'Arithmetic Sequences and Finite Series', 'family': 'series', 'week': 29, 'unit': 10, 'unit_title': 'Sequences, Series & Discrete Growth', 'essential': 'How do recursive and explicit structures describe discrete change, accumulation, convergence, and financial or scientific processes?', 'project': 'Discrete Growth, Finance & Convergence Investigation'}
Find 3+7+11+15+19.
8. {'id': 'u10-l02', 'number': 2, 'title': 'Arithmetic Sequences and Finite Series', 'family': 'series', 'week': 29, 'unit': 10, 'unit_title': 'Sequences, Series & Discrete Growth', 'essential': 'How do recursive and explicit structures describe discrete change, accumulation, convergence, and financial or scientific processes?', 'project': 'Discrete Growth, Finance & Convergence Investigation'}
Find the sum of the first 8 terms of 2,6,18,…
9. {'id': 'u10-l02', 'number': 2, 'title': 'Arithmetic Sequences and Finite Series', 'family': 'series', 'week': 29, 'unit': 10, 'unit_title': 'Sequences, Series & Discrete Growth', 'essential': 'How do recursive and explicit structures describe discrete change, accumulation, convergence, and financial or scientific processes?', 'project': 'Discrete Growth, Finance & Convergence Investigation'}
Does 12+6+3+… converge?
10. {'id': 'u10-l02', 'number': 2, 'title': 'Arithmetic Sequences and Finite Series', 'family': 'series', 'week': 29, 'unit': 10, 'unit_title': 'Sequences, Series & Discrete Growth', 'essential': 'How do recursive and explicit structures describe discrete change, accumulation, convergence, and financial or scientific processes?', 'project': 'Discrete Growth, Finance & Convergence Investigation'}
Evaluate Σ_{k=1}^{4} k².
11. {'id': 'u10-l02', 'number': 2, 'title': 'Arithmetic Sequences and Finite Series', 'family': 'series', 'week': 29, 'unit': 10, 'unit_title': 'Sequences, Series & Discrete Growth', 'essential': 'How do recursive and explicit structures describe discrete change, accumulation, convergence, and financial or scientific processes?', 'project': 'Discrete Growth, Finance & Convergence Investigation'}
Find the coefficient of x² in (1+x)^5.
12. {'id': 'u10-l02', 'number': 2, 'title': 'Arithmetic Sequences and Finite Series', 'family': 'series', 'week': 29, 'unit': 10, 'unit_title': 'Sequences, Series & Discrete Growth', 'essential': 'How do recursive and explicit structures describe discrete change, accumulation, convergence, and financial or scientific processes?', 'project': 'Discrete Growth, Finance & Convergence Investigation'}
State the convergence condition for an infinite geometric series.