Mathematics

Mathematics

Problem

A sequence is defined by un=12−3nu_n = 12 - 3n for natural numbers nn. Write down u1,u2,u_1, u_2, and u3u_3 and verify that the sequence is an arithmetic progression.
Intuitive explanation

This is about recognizing arithmetic progressions — sequences where consecutive terms differ by a constant amount. The key insight is that once you substitute each value of nn into the formula, you just need to check that the gaps between consecutive terms are all equal. That constant difference is what defines an arithmetic sequence and makes it predictable.

Intuitive explanation

This is about recognizing arithmetic progressions — sequences where consecutive terms differ by a constant amount. The key insight is that once you substitute each value of nn into the formula, you just need to check that the gaps between consecutive terms are all equal. That constant difference is what defines an arithmetic sequence and makes it predictable.

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