Finite Geometric Series (Grade 12 NSC Matric Mathematics): Quizzes

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Finite Geometric Series
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What is a finite geometric series?

Sum of specific number of geometric terms

In a geometric sequence, how is each term obtained from the previous term?

Multiply by the common ratio

In the formula Tn=a⋅r(n−1)T_n = a \cdot r^{(n-1)}, what does aa represent?

The first term

Why is the exponent (n−1)(n-1) in Tn=a⋅r(n−1)T_n = a \cdot r^{(n-1)} instead of nn?

First term already represents r0=1r^0 = 1

Which sum formula is more convenient when the common ratio r<1r < 1?

Sn=a(1−rn)1−rS_n = \frac{a(1 - r^n)}{1 - r}

Which sum formula is more convenient when the common ratio r>1r > 1?

Sn=a(rn−1)r−1S_n = \frac{a(r^n - 1)}{r - 1}

What is the critical condition for both sum formulas?

r≠1r \neq 1

What is the sum when r=1r = 1 in a geometric series?

n×an \times a

What happens to the series when the common ratio is negative?

Alternating positive and negative terms

How do you find the common ratio rr from consecutive terms?

r=T2T1r = \frac{T_2}{T_1}

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