Number series (next term by repeated ×4 − 1 rule): Determine the next value. Given sequence: 2, 7, 27, 107, 427, ? Pattern hint: each term equals (previous term × 4) − 1. Choose the correct next number.

Given data2, 7, 27, 107, 427, ?

Concept/ApproachTest a simple linear recurrence of the form a_n+1 = 4a_n − 1.

Step-by-step2 × 4 − 1 = 77 × 4 − 1 = 2727 × 4 − 1 = 107107 × 4 − 1 = 427Next: 427 × 4 − 1 = 1708 − 1 = 1707

VerificationThe rule holds for every transition; applying once more yields 1707.