Geometric Sequences (Grade 12 NSC Matric Mathematics): Quizzes

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Geometric Sequences
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What defines a geometric sequence?

Each term = previous term × constant ratio

How do you find the constant ratio rr in a geometric sequence?

Divide any term by the term before it

What is the general term formula for a geometric sequence?

Tn=arn−1T_n = ar^{n-1}

Why is the power (n−1)(n-1) used in Tn=arn−1T_n = ar^{n-1}, not nn?

Because the first term has power 0: T1=a×r0T_1=a×r^0

How do you test if a sequence is geometric?

Check if all consecutive ratios are equal

For sequence Tn=3×2n−1T_n = 3 × 2^{n-1}, what is T5T_5?

4848

What is the geometric mean formula for sequence a,x,ba, x, b?

x=±abx = ±\sqrt{ab}

Why can the geometric mean between two numbers be positive OR negative?

Both create valid geometric sequences

What is the key difference between arithmetic and geometric sequences?

Geometric multiplies, arithmetic adds

Is the sequence 3,9,27,813, 9, 27, 81 geometric?

Yes, r=3r = 3 (all ratios equal)

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