Recursive and Explicit Forms (Grade 11)
Free printable Grade 11 General Mathematics worksheet: converting between a recurrence relation and the explicit nth-term rule for arithmetic and geometric sequences (ACMGM069, ACMGM073).
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Grade 11 · Math worksheet
Name
Date
Math
Growth & Decay: Recursive and Explicit Forms
Convert between the recurrence relation and the explicit nth-term rule. Arithmetic: a(n) = a(1) + (n - 1)d. Geometric: a(n) = a(1) x r^(n-1). Also classify a rule as arithmetic or geometric.
- 1.An arithmetic sequence is defined by a(1) = 9 and a(n+1) = a(n) + 7. Write an explicit rule for a(n) in the form a(n) = 7n + c.
- 2.An arithmetic sequence is defined by a(1) = 12 and a(n+1) = a(n) + 7. Write an explicit rule for a(n) in the form a(n) = 7n + c.
- 3.An arithmetic sequence is defined by a(1) = 6 and a(n+1) = a(n) - 9. Write an explicit rule for a(n) in the form a(n) = -9n + c.
- 4.A geometric sequence is defined by a(1) = 2 and a(n+1) = 4 x a(n). Write an explicit rule for a(n).
- 5.A geometric sequence is defined by a(1) = 3 and a(n+1) = 4 x a(n). Write an explicit rule for a(n).
- 6.A geometric sequence is defined by a(1) = 2 and a(n+1) = 3 x a(n). Write an explicit rule for a(n).
- 7.A sequence has the explicit rule a(n) = 2 x . Is it arithmetic or geometric, and what is its recurrence relation (state a(1) and a(n+1))?
- 8.A sequence has the explicit rule a(n) = 3 x . Is it arithmetic or geometric, and what is its recurrence relation (state a(1) and a(n+1))?
- 9.A sequence has the explicit rule a(n) = 2 x . Is it arithmetic or geometric, and what is its recurrence relation (state a(1) and a(n+1))?
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