Geometric Sequences by Recursion (Grade 11)
Free printable Grade 11 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 11 · 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) = 4 and the recurrence relation a(n+1) = 2 x a(n). List the first 6 terms.
- 2.A sequence is defined by a(1) = 324 and the recurrence relation a(n+1) = 13 x a(n). List the first 5 terms.
- 3.A sequence is defined by a(1) = 5 and the recurrence relation a(n+1) = 3 x a(n). List the first 5 terms.
- 4.A sequence is defined by a(1) = 6 and the recurrence relation a(n+1) = 2 x a(n). List the first 6 terms.
- 5.A geometric sequence has first term a(1) = 6 and common ratio r = 3. Find the 9th term a(9).
- 6.A geometric sequence has first term a(1) = 2 and common ratio r = 3. Find the 7th term a(7).
- 7.A geometric sequence has first term a(1) = 5 and common ratio r = 2. Find the 8th term a(8).
- 8.The geometric sequence 2, 4, 8, 16, ... is generated by a recurrence relation. State the common ratio r.
- 9.The geometric sequence 5, 20, 80, 320, ... is generated by a recurrence relation. State the common ratio r.
- 10.The geometric sequence 4, 16, 64, 256, ... is generated by a recurrence relation. State the common ratio r.
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