ConceptFunctions & Sequences
← All conceptsArithmetic and geometric sequences
9 ways this goes wrong. Each one is a named misconception the questions are built to catch.
- Arithmetic/geometric formula mixedUses the arithmetic term/sum formula for a geometric sequence or vice versa.→
- Common ratio misidentifiedDerives the wrong common ratio from a given term.→
- Extremal-sum index off by oneLocates the maximizing/last-positive index off by one.→
- Geometric monotonicity q-sign ignoredIgnores negative-ratio or q-in-(0,1) vs q>1 cases when judging monotonicity sufficiency/necessity.→
- Geometric-sum offset not cancelledForgets that Sn=a·bn+c requires a+c=0 for a true geometric series.→
- Ratio exponent off by oneUses n instead of n-1 (or similar) in the geometric general-term exponent.→
- Sn treated as linearTreats the arithmetic partial sum as linear rather than quadratic in n when maximizing.→
- Symmetric-sum pairing misusedMisuses Sn=n(a1+an)/2 pairing when reasoning about sign or extremal partial sums.→
- Zero-crossing sign reasoning wrongDraws the wrong sign conclusion for terms around where the sequence crosses zero.→
