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.

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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.

Accepted Answer

Given data 2, 7, 27, 107, 427, ? Concept/Approach Test a simple linear recurrence of the form an+1 = 4an − 1. Step-by-step 2 × 4 − 1 = 77 × 4 − 1 = 2727 × 4 − 1 = 107107 × 4 − 1 = 427Next: 427 × 4 − 1 = 1708 − 1 = 1707 Verification The rule holds fo…

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.

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