A pattern with a constant ratio between terms. CAPS Grade 12 definition, worked NSC example and related sequences practice.
A pattern with a constant ratio between terms.
A geometric sequence multiplies each term by the same constant ratio r. Its general term is Tₙ = a·rⁿ⁻¹, and it converges only when −1 < r < 1.
2; 6; 18; 54 … has a = 2 and r = 3, so T₆ = 2(3)⁵ = 486.
Find n if 3; 6; 12; … has a term equal to 768: 3·2ⁿ⁻¹ = 768, so 2ⁿ⁻¹ = 256 = 2⁸ and n = 9.
Paper 1 asks for a specific term, the value of n, or the sum Sₙ = a(rⁿ − 1)/(r − 1), often using logarithms to solve for n.
Writing a·rⁿ instead of a·rⁿ⁻¹ for the general term.
A geometric sequence multiplies each term by the same constant ratio r. Its general term is Tₙ = a·rⁿ⁻¹, and it converges only when −1 < r < 1.
Geometric sequence belongs to the Sequences section of CAPS Grade 12 Mathematics, which is examined in Paper 1.
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