answer:Given that a_{10}=33 and a_2=1, we have an arithmetic sequence where the 10th term and the 2nd term are known. We can use the definition of an arithmetic sequence, which states that each term is equal to the previous term plus a common difference d. Thus, we can express the 10th term as: a_{10}=a_2+8d. Substituting the given values, we get: 33 = 1 + 8d, which gives us the common difference: d = frac{33 - 1}{8} = frac{32}{8} = 4. Additionally, using the property of arithmetic sequences that a_n=a_1+(n-1)d, where a_1 is the first term, we can find the first term of the sequence by considering the 2nd term: a_2 = a_1 + 1d = 1, which implies: a_1 = 1 - 4 = -3. Having both the first term and the common difference, we can apply the formula for the sum of the first n terms of an arithmetic sequence: S_n = frac{n}{2}(2a_1 + (n-1)d). Using this, we find the sum of the first 20 terms: S_{20} = frac{20}{2}[2(-3) + (20-1)4] = 10[-6 + 19(4)] = 10[-6 + 76] = 10[70] = 700. Similarly, for the sum of the first 10 terms: S_{10} = frac{10}{2}(2(-3) + (10-1)4) = 5[-6 + 9(4)] = 5[-6 + 36] = 5[30] = 150. So we need to calculate S_{20}-2S_{10}: S_{20}-2S_{10} = 700 - 2(150) = 700 - 300 = 400. Therefore, the final answer is: boxed{400}

answer:Let's break down the time it took for Jason to reach each rank: 1. It took him 8 years to reach the rank of chief. 2. To go from chief to senior chief, it took 25% longer than the 8 years. So, we calculate 25% of 8 years and add it to the 8 years: 25% of 8 years = 0.25 * 8 = 2 years Time to go from chief to senior chief = 8 years + 2 years = 10 years 3. To go from senior chief to master chief, it took 10% less time than it took to go from chief to senior chief. So, we calculate 10% of 10 years and subtract it from the 10 years: 10% of 10 years = 0.10 * 10 = 1 year Time to go from senior chief to master chief = 10 years - 1 year = 9 years 4. To go from master chief to command master chief, it took 50% longer than the 9 years. So, we calculate 50% of 9 years and add it to the 9 years: 50% of 9 years = 0.50 * 9 = 4.5 years Time to go from master chief to command master chief = 9 years + 4.5 years = 13.5 years Now, let's add up all the time it took for Jason to reach each rank and the additional 5 years after his last promotion before retiring: Time to reach chief + Time to senior chief + Time to master chief + Time to command master chief + Additional 5 years = 8 years + 10 years + 9 years + 13.5 years + 5 years = 45.5 years Finally, we add the time spent in the military to his age when he joined: Age when joined + Time spent in the military = 18 years + 45.5 years = 63.5 years Since we can't have a half year in age, we'll round down to the nearest whole year. Jason was boxed{63} years old when he retired.

answer:**Key Points:** Monotonicity of composite functions; properties and graphs of logarithmic functions. **Topic:** Properties and applications of functions. **Analysis:** Discuss in cases, using the monotonicity of composite functions, properties of logarithmic and quadratic functions to find the range of a, and synthesize to reach a conclusion. When a > 1, from 2 - a > 0, we get a < 2, thus 1 < a < 2. When 0 < a < 1, since 2 - ax can be negative on (-infty, 1], it does not satisfy the condition. In summary, we get 1 < a < 2, Therefore, the correct choice is: boxed{A}. **Review:** This question mainly examines the monotonicity of composite functions, properties of logarithmic and quadratic functions, reflecting the mathematical idea of transformation, and is considered a basic question.

answer:From the equation S_{n+1}+S_{n-1}=2(S_n+S_1), we can derive that (S_{n+1}-S_n)-(S_n-S_{n-1})=2S_1=2. This implies that a_{n+1}-a_n=2 for ngeq2. Therefore, the sequence {a_n} forms an arithmetic sequence starting from the second term. Hence, S_5=1+2+4+6+8=boxed{21}.