An arithmetic sequence a_n has a_1 = 2 and common difference d = 3. A sequence b_n is formed by b_n = 2^(a_n). Find the product P = b_1 b_2 ... * b_10.
Answer and explanation
Correct answer: D. 2^155
- Step 1: The product P = 2^(a_1 + a_2 + ... + a_10).
- Step 2: The sum S_10 is the sum of the first 10 terms of an arithmetic progression.
- Step 3: S_10 = (10 / 2) (2a_1 + (10 - 1)d) = 5 (22 + 93) = 5 (4 + 27) = 5 31 = 155.
- Step 4: Therefore, P = 2^155.
Answer
2^155.
Why not the others: 2^140 uses 9 terms instead of 10; 2^170 miscalculates 5 34; 2^125 computes 5 25.
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