Find the next number of the series. 563, 647, 479, 815, ...?

In a number series built from differences that themselves form a pattern, each difference between consecutive terms can follow its own rule — here, a geometric progression where each difference is obtained by multiplying the previous difference by a fixed ratio, with the sign alternating.

1. Find the difference between each pair of consecutive terms: 647 − 563 = +84; 479 − 647 = −168; 815 − 479 = +336.

2. Compare consecutive differences: −168 ÷ 84 = −2, and 336 ÷ (−168) = −2 — each difference is the previous one multiplied by −2, i.e., the magnitude doubles and the sign alternates.

3. Apply the same ratio to get the next difference: 336 × (−2) = −672.

4. Add this difference to the last given term: 815 + (−672) = 143.

Cross-check: the ratio between consecutive differences is constant at −2 throughout (84 → −168 → 336 → −672), confirming the pattern holds consistently rather than being a coincidental fit for only three terms.

Hence, the next number in the series is 143.