Sequences & Series
Sequences & Series (AP/GP)
Sequences & Series covers Arithmetic Progressions (AP) and Geometric Progressions (GP) — two fundamental patterns found in competitive exam number series, word problems, and sum questions. Identifying which type applies is the first and most important step.
Key Idea
AP: constant difference. GP: constant ratio. Check which one applies first. For AP sum, the fastest form is n/2 × (first + last).
Core Formulas
AP nth term
aₙ = a + (n−1)d
To find any term of an arithmetic progression
AP Sum
Sₙ = n/2 × (first + last) or n/2 × [2a + (n−1)d]
To find sum of n terms of AP
GP nth term
aₙ = a × r^(n−1)
To find any term of a geometric progression
GP Sum (finite)
Sₙ = a(rⁿ − 1)/(r − 1) for r > 1; a(1 − rⁿ)/(1 − r) for r < 1
To find sum of n terms of GP
Sum of first n naturals
Sₙ = n(n+1)/2
Instant sum without adding term by term
Relevant Exams
3–5 questions in SSC CGL Tier 1 and banking exams. Number series questions in IBPS PO pre test 5 patterns per set. Sum of AP/GP in SSC Tier 2 and CDS.