Arithmetic Progression Essentials
Medium-level multiple-choice quiz covering definitions, formulas, applications, and common misconceptions about arithmetic progressions.
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Quiz Questions & Answers
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Question 1: What best defines an arithmetic progression (AP)?
A sequence of random numbers with no pattern
A sequence where each term increases by the same fixed difference
A sequence where differences between terms grow linearly
A sequence where each term is multiplied by a constant ratio
Question 2: Given first term a1 and common difference d, what is the nth term formula?
an = a1 · d^(n-1)
an = a1 + n·d
an = a1 + (n - 1)·d
an = (a1 + d) / n
Question 3: Which formula gives the sum of the first n terms (Sn) of an AP?
Sn = n·a1 · an
Sn = n·(a1 + an)/2
Sn = (a1 + an)/n
Sn = n·a1 + d·n
Question 4: If a1 = 5 and d = -2, what happens to the sequence as n grows?
Terms oscillate between two values
Terms decrease linearly and will eventually be negative large in magnitude
Terms converge to a finite limit
Terms form a geometric progression instead
Question 5: You know a5 = 20 and a12 = 48. What is the common difference d?
4
2
8
28
Question 6: Which scenario is NOT an arithmetic progression?
2, 4, 8, 16
10, 7, 4, 1
0, 0, 0, 0
3, 7, 11, 15
Question 7: Why is the average of any two symmetric terms in an AP equal to the middle term?
Because APs always have zero mean
Because terms are linear so symmetric positions sum to twice the central term
Because of the geometric ratio between terms
Because only odd-length sequences have this property
Question 8: Common myth: every sequence with constant second differences is an AP. Is this true?
No — constant second differences imply a quadratic sequence, not necessarily an AP
Only for infinite sequences
Yes — constant second differences always mean linear growth
Only if the first term is zero