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📐 Mathematics  ·  Sequences and Series  ·  JEE

The sum 2 + 2² + 2³ + ... + 2<sup>n</sup> =

Answer: 2 n+1 - 2.

  • A 2<sup>n+1</sup> - 2
  • B 2<sup>n</sup> - 1
  • C 2<sup>n+1</sup>
  • D 2(2<sup>n</sup> - 1)

Correct answer: A. 2<sup>n+1</sup> - 2

Explanation: GP with first term a=2, ratio r=2, n terms. Sum = a(rⁿ−1)/(r−1) = 2(2ⁿ−1)/1 = 2·2ⁿ−2 = 2<sup>n+1</sup>−2.

Each bar grows by the common difference d=3a1=2a2=5a3=8a4=11d=3

Bar heights for AP 2, 5, 8, 11 with the common difference d=3 marked between consecutive terms.

Concept context

Arithmetic progressions, geometric progressions, and sums

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