📐 Mathematics · Sequences and Series · JEE

The value of 1·2 + 2·2² + 3·2³ + ... + 5·2⁵ (that is Σ n·2ⁿ for n = 1 to 5) is:

Answer: 258.

Correct answer: B. 258

Explanation: Σ n·2ⁿ = (n−1)2<sup>n+1</sup> + 2. For n = 5: 4·64 + 2 = 258. Direct sum: 2+8+24+64+160 = 258.

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