Recursion With Geometric Sequences (VCE SSCE General Mathematics): Quizzes

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Recursion With Geometric Sequences
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10 questions from this quiz

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What two things does a recurrence relation tell you?

Starting value and rule

For t0=5,tn+1=2tnt_0 = 5, t_{n+1} = 2t_n, what is the starting value?

5

For t0=2,tn+1=3tnt_0 = 2, t_{n+1} = 3t_n, what is the common ratio?

3

Given t0=5,tn+1=2tnt_0 = 5, t_{n+1} = 2t_n, what is t1t_1?

10

In the general form t0=a,tn+1=Rtnt_0 = a, t_{n+1} = Rt_n, what does RR represent?

Common ratio

What is the direct formula for the nth term of a geometric sequence?

tn=Rn×at_n = R^n \times a

For t0=2,tn+1=3tnt_0 = 2, t_{n+1} = 3t_n, what is t12t_{12}?

1,062,882

In tn=Rn×at_n = R^n \times a, what does the exponent nn represent?

Number of times rule applied

Given t0=1,tn+1=4tnt_0 = 1, t_{n+1} = 4t_n, what is t3t_3?

64

Why is the direct formula more efficient than using the recurrence relation?

Find any term without all previous ones

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