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Algebra · SS2

Sequences & series (AP, GP)

Number patterns that grow by adding (arithmetic) or multiplying (geometric), their terms and sums.

Before this
Expressions, formulae & change of subject
Leads to
Sequences, series & binomial expansion

Learn

  1. 1Sequences and arithmetic progressionsThe nth term of a sequence, arithmetic progressions and the formula Tₙ = a + (n − 1)d, finding a and d from two terms, counting terms, and three consecutive terms.Done16 min
  2. 2The sum of an arithmetic progressionAdding the terms of an A.P. with Sₙ = n/2 [2a + (n − 1)d] or n/2 (a + l): finding the sum, finding a and d from a term and a sum, and finding how many terms give a sum.Done15 min
  3. 3Geometric progressionsGeometric progressions and the formula Tₙ = arⁿ⁻¹, finding a and r from two terms by dividing, the two ratios an even power gives, and three consecutive terms.Done15 min
  4. 4The sum of a G.P. and the sum to infinityAdding the terms of a G.P. with Sₙ = a(rⁿ − 1)/(r − 1), why the sum goes on for ever only when r is between −1 and 1, and the sum to infinity S∞ = a/(1 − r).Done14 min

Practise

Answer sequences & series (ap, gp) questions one at a time. You'll know straight away whether you're right, with hints and the working step by step.

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Past questions (97)

From 1987–2025: 38 WAEC, 11 NECO, 48 JAMB. Theory questions first, then objective, newest first.

Theory (32)

Objective (65)