Find the wrong term in the series 3, 7, 15, 27, 63, 127.

In a wrong-term question, most of the series follows the rule and one term breaks it. Find the rule using the terms that look reliable, often the first two and the last two. Here 63 to 127 and 3 to 7 both fit "double and add 1", which tells you the rule; then test each term against it.

Question: 3, 7, 15, 27, 63, 127. Which term is wrong?

1. Try "x 2 + 1": 3 to 7, 7 to 15, 15 to 31 (not 27), 31 to 63, 63 to 127.
2. Only 27 breaks the rule, and replacing it with 31 makes the rest fit.
3. Wrong term = 27 (correct value 31).

Another view: the terms are 2^2 - 1, 2^3 - 1, 2^4 - 1, 2^5 - 1, 2^6 - 1, 2^7 - 1.

const s = [3];
for (let i = 0; i < 5; i++) s.push(s[s.length - 1] * 2 + 1);
console.log(s); // Output: [3,7,15,31,63,127]

Check your rule against both neighbours of the suspect term. If 27 were right, 27 x 2 + 1 = 55 should follow, but 63 does.

• Choosing 63 as wrong because 27 to 63 does not fit; the fault lies with the term that breaks the rule on both sides.
• Settling on a rule after checking only the first two terms.