3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =
A. 3^7
B. 3^8
C. 3^14
D. 3^28
E. 3^30
Always look at the answer choices BEFORE you start to work.
Here, the answer choices are SPREAD OUT.
Thus, we can quickly BALLPARK the correct answer.
Since the greatest term = 2 * 3�, the sum of ALL the terms must be GREATER than 3�.
Eliminate A.
2 * 3� = 2 * 3³ * 3� = 2 * 27 * 81 ≈ 60*80 = 4800.
2 * 3� = (2 * 3�)/3 = 4800/3 = 1600.
2 * 3� = (2 * 3�)/3 ≈ 1600/3 ≈ 500.
The terms to the left of 2 * 3� will be relatively small and thus will have little effect on the final sum.
For example, 2 * 3� = 2*81 = 162, which is very small relative to the other values (4800, 1600, and 500).
Thus, we can ignore the remaining terms when we approximate the sum, implying that the correct answer ≈ 4800+1600+500 = 7000.
Look at the remaining answer choices.
C: 3¹� = 3� * 3� * 3� * 3² = 81*81*81*9 ≈ 80*80*80*10.
Thus, answer choices C, D and E are WAY too big.
The correct answer is
B.
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