Geometric Progressions — O/L Mathematics

What must I remember about Geometric Progressions?

• Geometric Progression (GP): Sequence of numbers where each term after the first is obtained by multiplying the previous term by a fixed non-zero constant called the Common Ratio (r).
• Common Ratio: r = T2 / T1 = T3 / T2 = T_n / T_n-1.
• General nth Term (T_n): T_n = a * r^n-1, where a is the first term and r is the common ratio.
• Sum of First n Terms (S_n): For r ≠ 1: S_n = [ a (rⁿ - 1) ] / (r - 1) when r > 1; S_n = [ a (1 - rⁿ) ] / (1 - r) when r < 1.

Test yourself (1 minute)

1. Indices manipulation

   When solving T_n = a r^n-1, express both sides with matching prime bases to equate exponents (e.g., 2^n-1 = 64 = 2⁶ => n - 1 = 6 => n = 7).

2. Negative common ratio

   When r < 0, terms oscillate alternately in sign (+, -, +, -, ...); compute powers of negative numbers carefully (e.g., (-2)³ = -8, (-2)⁴ = +16).

3. Geometric Mean

   For three terms a, b, c in GP: b / a = c / b => b² = ac => b = √(ac).

Practise Geometric Progressions questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 11, Unit 16)

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Where does Geometric Progressions fit in the syllabus?

Grade 11 · Term 2