Which of the following numbers will replace the question mark (?) and complete the given number series? 4, 5, 12, 39, 160, ?

Explanation

4, 5, 12, 39, 160, ? To find the pattern, let's examine how each term relates to the previous term. 4 to 5: Add 1 5 to 12: Multiply by 2 and add 2 (5 × 2 + 2 = 12) 12 to 39: Multiply by 3 and add 3 (12 × 3 + 3 = 39) 39 to 160: Multiply by 4 and add 4 (39 × 4 + 4 = 160) We observe a pattern: each term is multiplied by an increasing integer (2, 3, 4, ...) and then the same integer is added to the result. Calculate the Next Term Following the pattern, to get the next term, we multiply the last term (160) by 5 and add 5: 160 × 5 + 5 = 800 + 5 = 805 Final Answer The number that will replace the question mark in the series is 805.