Geometric Sequences by Recursion (Grade 12)
Free printable Grade 12 General Mathematics worksheet: geometric sequences generated by a recurrence relation a(n+1) = r x a(n), modelling exponential growth and decay. Answers computed from the recurrence (ACMGM071-074).
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Grade 12 · Math worksheet
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Date
Math
Growth & Decay: Geometric Sequences by Recursion
Use each geometric recurrence relation a(n+1) = r x a(n). List terms, find the nth term with the rule a(n) = a(1) x r^(n-1), or read off the common ratio.
- 1.A sequence is defined by a(1) = 3 and the recurrence relation a(n+1) = 2 x a(n). List the first 5 terms.
- 2.A sequence is defined by a(1) = 3 and the recurrence relation a(n+1) = 3 x a(n). List the first 5 terms.
- 3.A sequence is defined by a(1) = 6 and the recurrence relation a(n+1) = 3 x a(n). List the first 5 terms.
- 4.A sequence is defined by a(1) = 1 and the recurrence relation a(n+1) = 2 x a(n). List the first 5 terms.
- 5.A geometric sequence has first term a(1) = 6 and common ratio r = 3. Find the 5th term a(5).
- 6.A geometric sequence has first term a(1) = 6 and common ratio r = 3. Find the 6th term a(6).
- 7.A geometric sequence has first term a(1) = 6 and common ratio r = 2. Find the 5th term a(5).
- 8.The geometric sequence 3, 6, 12, 24, ... is generated by a recurrence relation. State the common ratio r.
- 9.The geometric sequence 3, 6, 12, 24, ... is generated by a recurrence relation. State the common ratio r.
- 10.The geometric sequence 2, 6, 18, 54, ... is generated by a recurrence relation. State the common ratio r.
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