Arithmetic Sequences by Recursion (Grade 12)
Free printable Grade 12 General Mathematics worksheet: arithmetic sequences generated by a recurrence relation a(n+1) = a(n) + d, modelling linear growth and decay. Every term computed by running the recurrence (ACMGM067-070).
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Grade 12 · Math worksheet
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Math
Growth & Decay: Arithmetic Sequences by Recursion
Use each arithmetic recurrence relation a(n+1) = a(n) + d. List terms, find the nth term with the rule a(n) = a(1) + (n - 1)d, or read off the common difference.
- 1.A sequence is defined by a(1) = 100 and the recurrence relation a(n+1) = a(n) - 6. List the first 6 terms.
- 2.A sequence is defined by a(1) = 18 and the recurrence relation a(n+1) = a(n) + 5. List the first 5 terms.
- 3.A sequence is defined by a(1) = 68 and the recurrence relation a(n+1) = a(n) - 6. List the first 6 terms.
- 4.A sequence is defined by a(1) = 8 and the recurrence relation a(n+1) = a(n) + 6. List the first 6 terms.
- 5.An arithmetic sequence has first term a(1) = 3 and common difference d = -4. Find the 8th term a(8).
- 6.An arithmetic sequence has first term a(1) = 13 and common difference d = 3. Find the 17th term a(17).
- 7.An arithmetic sequence has first term a(1) = 8 and common difference d = 8. Find the 19th term a(19).
- 8.An arithmetic sequence has first term a(1) = 6 and common difference d = -6. Find the 17th term a(17).
- 9.The arithmetic sequence 3, 5, 7, 9, ... is generated by a recurrence relation. State the common difference d.
- 10.The arithmetic sequence 7, 12, 17, 22, ... is generated by a recurrence relation. State the common difference d.
- 11.The arithmetic sequence 16, 5, -6, -17, ... is generated by a recurrence relation. State the common difference d.
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