On a ladder, each next rung is (6) cm higher than the previous one. The heights are (10,16,22,28,\ldots). What do they form?

Correct answer: Arithmetic progression

The direct answer is option D: an arithmetic progression. An arithmetic progression, or AP, is a sequence in which the difference between every pair of consecutive terms is the same. The heights are 10, 16, 22, 28, and so on. Calculate the consecutive differences step by step: \(16-10=6\), \(22-16=6\), and \(28-22=6\). Since the common difference is always 6 cm, the sequence is an AP with first term \(a=10\) and common difference \(d=6\). Option D is correct. Option A, a geometric progression, would require a constant ratio, not a constant difference. Here the ratios are \(16/10\), \(22/16\), and \(28/22\), which are not equal. Option B, a simple list, is not the best mathematical classification because the terms follow a clear fixed-difference rule. Option C, no sequence, is wrong because a sequence is simply an ordered list of terms, and these heights are clearly ordered. The ladder story tells us exactly why the difference is constant: each next rung is 6 cm higher than the previous one. A positive common difference means the AP increases. Do not confuse equal addition with equal multiplication. Memory cue: AP means add the same number each time; GP means multiply by the same number.