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Tip 1 For regular difference and ratio sequences, the first two questions in the exam are usually of this type.
When the sequence is neat and shows an increasing or decreasing trend, prioritize using differences.
2016 Jiangsu Province Public Exam Quantitative Real Question: 2, 7, 14, 25, 38, ( )
A 54 B 55 C 57 D 58
[Analysis] After taking the differences, we get 5, 7, 11, 13, which is a prime number sequence. The next term is 17, so 38 + 17 = 55, choose B.
When there is a clear multiplicative relationship between terms, prioritize using ratios.
2017 Jiangsu Province Public Exam Quantitative Real Question: -1, 3, -3, -3, -9, ( )
A -9 B -4 C -14 D -45
[Analysis] The next term is -3 times the previous term. The differences are -1, 1, 3, with a common difference of 2, so the next term is 5, thus -9 * 5 = -45, choose D.
2017 Zhejiang Province Public Exam Quantitative Real Question: 3, 3, 6, 18, ( )
A 54 B 72 C 90 D 108
[Analysis] The subsequent terms are derived from the previous terms with a common difference of 1, so the next term is 4, thus 18 * 4 = 72, choose B.
Tip 2: For numbers with decimal points, prioritize separating the numbers before and after the decimal for calculation.
2017 Jiangsu Province Public Exam Quantitative Real Question: 4.1, 4.3, 12.1, 12.11, 132.1, ( )
A 120.8 B 124.12 C 132.131 D 132.12
[Analysis] Observing the sequence, the last term is derived from the previous term’s numbers. The part before the decimal is multiplied for the first part, and subtracted for the second part. Thus, the answer is 132 * 1 for the front part and 132 – 1 for the back part, resulting in 132.131, choose C.
2016 Jiangsu Province Public Exam Quantitative Real Question: 4.2, 5.2, 8.4, 17.8, 44.22, ( )
A 125.62 B 85.26 C 99.44 D 125.64
[Analysis] Observing the odd terms, the number before the decimal is twice the number after the decimal. The even terms’ front number is twice the back number plus one. The answer for the sixth term, which is an even term, must be 125.62, satisfying the 2 times plus 1 rule, choose A.
2015 Jiangsu Province Public Exam Quantitative Real Question: 2.3, 4.8, 8.24, 16.51, 32.89, ( ).
A 64.138 B 64.136 C 128.138 D 128.136
[Analysis] Observing the sequence, the numbers before the decimal form a clear geometric sequence. The front part before the bracket is 64, and the back part shows an increasing trend. The answer is 64.138, choose A.
Tip 3 Prime and composite number sequences are important exam points. A prime number is a positive integer that cannot be divided by any number other than 1 and itself.
Prime numbers: 2, 3, 5, 7, 11, 13…….
Composite numbers: 4, 6, 8, 9, 10, 12…….
2010 Jiangsu Province Public Exam Quantitative Real Question: 5, 7, 11, 15, 23, ( )
A 25 B 27 C 28 D 31
[Analysis] The differences do not show a clear pattern, consider the prime number sequence. 5=2*2+1, 7=3*2+1, 11=5*2+1, 15=7*2+1, 23=11*2+1, hence the bracket must be 13*2+1=27, choose B.
Tip 4 Split thinking
2013 Jiangsu Province Public Exam Quantitative Real Question: 12, 23, 35, 47, 511, ( )
A 613 B 612 C 611 D 610
[Analysis] This question shows an increasing trend, but the second to last term increases suddenly, and there is no multiplicative relationship. Thus, splitting is necessary.
1｜2, 2｜3, 3｜5, 4｜7, 5｜11, the front part forms an arithmetic sequence with a common difference of 1, while the back part is a prime number sequence. Thus, the answer is 6｜13, choose A.
Tip 5 Power correction
Power correction sequences are also important exam points. For numbers under 10, squares and cubes must be memorized. If a number in the sequence is close to these, prioritize power correction.
2014 Jiangsu Province Public Exam Quantitative Real Question: 9, 30, 69, 132, 225, ( )
A 354 B 387 C 456 D 540
[Analysis] In the sequence, 30 and 69 are close to special numbers 27 and 64, indicating power correction. 9=2^3+1, 30=3^3+3, 69=4^3+5, 132=5^3+7, 225=6^3+9, thus the bracket must be 7^3+11=354, choose A.
2013 Jiangsu Province Public Exam Quantitative Real Question: 0, 5, 8, 17, 24, ( )
A. 37 B. 45 C. 51 D. 62
[Analysis] The sequence contains 17 and 24, which are close to special numbers 16 and 25, indicating power correction. 0=1^2-1, 5=2^2+1, 8=3^2-1, 17=4^2+1, 24=5^2-1, thus the bracket must be 62+1=37, choose A.
Tip 6 Grouped sequences
2015 Jilin Province Public Exam Quantitative Real Question: 3, 4, 5, 6, 8, ( )
A 9 B 10 C 12 D 15
[Analysis] The differences and sums show no clear pattern. Observing the sequence, there are 6 terms, which are even terms. Trying to group them, 4-3, 6-5, ?-8, the first two groups have a difference of 1, thus the bracket should be 9, choose A. The sequence is even terms, and when conventional methods yield no results, consider grouped operations.
Tip 7 Sequences with numbers above three digits
Sequences with numbers above three digits are generally large, and basic operations like addition, subtraction, multiplication, or division are rarely tested. Instead, focus on the operations on the digits.
2017 Guangdong Province Public Exam Quantitative Real Question: 325 118 721 604 ( )
A 911 B 541 C 431 D 242
[Analysis] Observing the sequence, the sum of the digits is 10 for each term. Among the options, A is 11, B is 10, C is 8, D is 8, only B satisfies the requirement.
2013 Jiangsu Province Public Exam Quantitative Real Question: 110, 484, 231, 352, 143, ( )
A 572 B 429 C 512 D 139
[Analysis] Observing the sequence, the ten’s place equals the hundred’s place plus the unit’s place, 7=5+2. Only option A satisfies this rule.
Tip 8 Flexibly observing the details of the problem
2017 Zhejiang Province Public Exam Quantitative Real Question: 80, 56, 52, 30, 37, ( )
A 21/2 B 11 C 23/2 D 12
[Analysis] Observing this question, two options have a denominator of 2 and the sequence shows a decreasing trend. Considering the difference after dividing the latter term by 2, we find that 80-56/2=52, 56-52/2=30, 52-30/2=37, thus the bracket = 30-37/2=23/2, the answer is C.