1. **Stating the problem:** You start selling an NFT at 5 and make a 10% profit per sale. The price increases until it reaches 150. From each profit, 1.5% is deducted. We want to find the total deduction by the time the price reaches 150. 2. **Understanding the problem:** Each sale increases the price by 10%, so the price after $n$ sales is given by the geometric sequence: $$P_n = 5 \times (1.10)^n$$ 3. **Finding the number of sales:** We want to find $n$ such that: $$5 \times (1.10)^n = 150$$ Divide both sides by 5: $$ (1.10)^n = 30$$ Take the natural logarithm: $$ n = \frac{\ln(30)}{\ln(1.10)} $$ Calculate: $$ n \approx \frac{3.4012}{0.0953} \approx 35.7 $$ Since $n$ must be an integer number of sales, we take $n=35$ (price just below 150) or $n=36$ (price just above 150). We use $n=36$ to reach or exceed 150. 4. **Calculating total profit:** The profit at each sale $k$ is the increase from previous price: $$ \text{Profit}_k = P_k - P_{k-1} = 5 \times (1.10)^k - 5 \times (1.10)^{k-1} = 5 \times (1.10)^{k-1} \times (1.10 - 1) = 5 \times (1.10)^{k-1} \times 0.10 $$ 5. **Total profit over $n=36$ sales:** $$ \text{Total Profit} = \sum_{k=1}^{36} 5 \times (1.10)^{k-1} \times 0.10 = 0.5 \times \sum_{k=0}^{35} (1.10)^k $$ The sum of a geometric series: $$ \sum_{k=0}^{n-1} r^k = \frac{r^n - 1}{r - 1} $$ So: $$ \sum_{k=0}^{35} (1.10)^k = \frac{(1.10)^{36} - 1}{1.10 - 1} = \frac{(1.10)^{36} - 1}{0.10} $$ 6. **Calculate $(1.10)^{36}$:** $$ (1.10)^{36} \approx 30.05 $$ 7. **Calculate total profit:** $$ \text{Total Profit} = 0.5 \times \frac{30.05 - 1}{0.10} = 0.5 \times \frac{29.05}{0.10} = 0.5 \times 290.5 = 145.25 $$ 8. **Calculate total deduction:** Deduction is 1.5% of total profit: $$ \text{Total Deduction} = 0.015 \times 145.25 = 2.17875 $$ **Final answer:** The total deduction by the time the NFT price reaches 150 is approximately $2.18$.