@coffeeandfun/maths-captcha/src/question-types/sequence.js

Maths-Captcha is a simple Node.js module that generates random math questions to verify human interaction. It creates math problems like addition, subtraction, multiplication, division, powers, percentages, sequences, and algebra, and checks if the user's

import { randomInt, randomChoice } from '../random.js';

const SEQUENCE_STYLES = ['arithmetic', 'geometric'];

export function generateSequence(config, options = {}) {
  const style = options.style ?? randomChoice(SEQUENCE_STYLES);
  return style === 'geometric'
    ? buildGeometric(config)
    : buildArithmetic(config);
}

function buildArithmetic(config) {
  const start = randomInt(1, 10);
  const step = randomInt(1, 9);
  const terms = [start, start + step, start + 2 * step, start + 3 * step];
  const next = start + 4 * step;

  return formatSequence(terms, next, [start, step], 'arithmetic');
}

function buildGeometric() {
  const start = randomInt(1, 4);
  const ratio = randomInt(2, 4);
  const terms = [
    start,
    start * ratio,
    start * ratio * ratio,
    start * ratio * ratio * ratio,
  ];
  const next = start * Math.pow(ratio, 4);

  return formatSequence(terms, next, [start, ratio], 'geometric');
}

function formatSequence(terms, next, operands, style) {
  return {
    question: `${terms.join(', ')}, ?`,
    answer: next.toString(),
    numericAnswer: next,
    operation: 'seq',
    operands,
    type: 'sequence',
    style,
  };
}