What is the sum of the first few centered hexagonal numbers, given the sequence 1, 7, 19, 37, ...?

April 10, 2026Mathematics

ScanSolve AI Answer

April 10, 2026

Answer

3n^2 - 3n + 1$.

Step 1: Identify the sequence being added. The question asks to add up the sequence $1, 7, 19, 37, \dots$ . These numbers are known as centered hexagonal numbers. The formula for the $n$ -th centered hexagonal number is $CH_n = 3n^2 - 3n + 1$ . Let's verify the first few terms: For $n=1$ : $CH_1 = 3(1)^2 - 3(1) + 1 = 3 - 3 + 1 = 1$ . For $n=2$ : $CH_2 = 3(2)^2 - 3(2) + 1 = 12 - 6

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Quick Answer

Identify the sequence being added. The question asks to add up the sequence 1, 7, 19, 37, .

Asked on April 10, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 10, 2026

Step 1: Identify the sequence being added. The question asks to add up the sequence 1, 7, 19, 37, . These numbers are known as centered hexagonal numbers. The formula for the n-th centered hexagonal number is CH_n = 3n^2 - 3n + 1. Let's verify the first few terms: For n=1: CH_1 = 3(1)^2 - 3(1) + 1 = 3 - 3 + 1 = 1. For n=2: $CH_2 = 3(2)^2 - 3(2) + 1 = 12 - 6