Generalization, model comparison, proof, and technology-assisted validation.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u10-l06', 'number': 6, 'title': 'Binomial Theorem and Pascal Structure', 'family': 'series', 'week': 30, '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.
2. {'id': 'u10-l06', 'number': 6, 'title': 'Binomial Theorem and Pascal Structure', 'family': 'series', 'week': 30, '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,…
3. {'id': 'u10-l06', 'number': 6, 'title': 'Binomial Theorem and Pascal Structure', 'family': 'series', 'week': 30, '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?
4. {'id': 'u10-l06', 'number': 6, 'title': 'Binomial Theorem and Pascal Structure', 'family': 'series', 'week': 30, '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.
5. {'id': 'u10-l06', 'number': 6, 'title': 'Binomial Theorem and Pascal Structure', 'family': 'series', 'week': 30, '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.
6. {'id': 'u10-l06', 'number': 6, 'title': 'Binomial Theorem and Pascal Structure', 'family': 'series', 'week': 30, '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.
7. {'id': 'u10-l07', 'number': 7, 'title': 'Discrete Modelling and Financial Applications', 'family': 'sequences', 'week': 30, '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,…
8. {'id': 'u10-l07', 'number': 7, 'title': 'Discrete Modelling and Financial Applications', 'family': 'sequences', 'week': 30, '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,…
9. {'id': 'u10-l07', 'number': 7, 'title': 'Discrete Modelling and Financial Applications', 'family': 'sequences', 'week': 30, '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}.
10. {'id': 'u10-l07', 'number': 7, 'title': 'Discrete Modelling and Financial Applications', 'family': 'sequences', 'week': 30, '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,…
11. {'id': 'u10-l07', 'number': 7, 'title': 'Discrete Modelling and Financial Applications', 'family': 'sequences', 'week': 30, '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?
12. {'id': 'u10-l07', 'number': 7, 'title': 'Discrete Modelling and Financial Applications', 'family': 'sequences', 'week': 30, '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).