🔢 AP & GP Series Visualizer - Arithmetic Geometric Progressions
SequencesWhat's happening? AP: each term adds d. GP: each term multiplies by r. GP converges when |r| < 1. Watch the bars grow linearly (AP) vs exponentially (GP).
Sequences: 3-5 questions every year.
JEE tests AP, GP, HP, AM-GM, infinite series.
Key formulas
AP & GP Series Formulas
AP nth
a_n = a + (n-1)d
First term a, common diff d
AP sum
S_n = n/2(2a+(n-1)d)
Sum of n terms
GP nth
a_n = a*r^(n-1)
First term a, ratio r
GP sum
S_n = a(r^n-1)/(r-1), S_inf = a/(1-r)
|r|<1 for infinite
Step-by-step problem solving
How to solve maths problems in JEE
- Identify AP or GP
- Find a, d (AP) or r (GP)
- Apply nth term formula
- Sum: S_n. Infinite: check |r|<1
Common JEE mistakes
What students get wrong
Infinite GP without |r|<1
Diverges if |r|>=1
AP vs GP
AP: add d. GP: multiply r
HP confusion
HP = 1/AP. Reciprocals in AP
AM-GM sign
AM >= GM. Equal only when all equal
FAQs
AP & GP Series Questions
AP vs GP?
AP: constant difference. GP: constant ratio
Infinite GP converge?
|r| < 1. Sum = a/(1-r)
AM, GM, HM?
AM >= GM >= HM
HP problems?
Convert to AP by reciprocals