Geometric Sequences (HSC SSCE Mathematics Advanced): Quizzes

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Geometric Sequences
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What is the defining feature of a geometric sequence?

Each term is obtained by multiplying

For the sequence 3,12,48,192,3, 12, 48, 192, \ldots, what is the common ratio rr?

r=4r = 4

Is the sequence 2,4,16,32,2, 4, 16, 32, \ldots a geometric progression?

No, ratios are 2,4,22, 4, 2 (not all equal)

What is the general formula for the nnth term of a geometric sequence?

Tn=arn1T_n = ar^{n-1}

In the formula Tn=arn1T_n = ar^{n-1}, why is the exponent n1n-1 rather than nn?

The power of rr is one less than term number

Why can zero never appear as a term in a geometric sequence?

It would make the next ratio undefined

What happens to a geometric sequence when the common ratio is negative?

Terms alternate between positive & negative

Find T5T_5 for the GP with a=2a = 2 and r=3r = 3.

T5=162T_5 = 162

Is 128128 a term in the sequence 2,8,32,2, 8, 32, \ldots?

Yes, it is T4T_4

How are geometric sequences related to exponential functions?

GPs are integer points on exponential graphs

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