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Sum of items in row-equal arithmetic series to solve problems

2019-12-27 10:16:52 | Source: CJ Education Zhou Jinnan

The equation of sum of equal difference series is often used in solving the calculation problem of line test, but after we have done many problems, we will find that in the process of using the sum formula, we must combine the general formula. Although the problem-solving idea is clear, Difficult to calculate answers quickly. And how to quickly solve the quantitative problem is exactly what we are pursuing. How to use the median sum formula to solve the problem quickly? Today , Cong Gong Education will work with you to find out.

Let's first look at a simple topic and see how to investigate this knowledge point.

[Example 1] There is a total of 25 rows of seats in the auditorium of a school. The latter row has 2 more seats than the previous row. It is known that there are 56 seats in the 13th row. How many seats are there in this theater?

A.1200 B.1400 C.1600 D.1800

[Answer] B. Chinese public analysis: The question is how many seats are there in the theater, and the title describes the second row has two more seats than the previous row. Combined with the definition of the equal difference series, it is clear that each row of the entire auditorium belongs to the equal difference series. This is the sum of the difference series. The number of items in the difference sequence is 25, then the middle term is 13, and the number of seats in the 13th row is known. We can use the sum of the odd terms to calculate the middle term. Multiply the number of terms by the middle term 25 * 56 = 1400 seats. Select B.

If we can solve the intermediate term in the problem solving process, if it is not given directly, must we calculate the intermediate term to solve it? You can come to the next question with me.

[Example 2] There are 25 rows of trees on a mountain, the latter row has 2 more trees than the previous row, and the last row has 70 trees. How many trees are there on this mountain?

A.1104 B.1150 C.1170 D.1280

[Answer] B. Zhonggong analysis: find how many trees there are in the mountain, and if the question says that the next row has 2 more trees than the previous row, then each row of trees on the hill is in the same number series. The summation formula with the middle term should be 25 times the middle term, then the tree must be divisible by 25, the mantissa must be 0 and 5 to exclude A, and it can be divided by B. It cannot be divided by C, and D cannot be divided by. So choose B.

So can we only use the median to sum up? Can we also use the median to solve the median? Let's continue to look at such a problem.

[Example 3] There are 8 questions in a test paper, each of which is 4 points more than the previous one. If the score is 120 points, the score of the fourth question is: ().

A.17 B.16 C.13 D.11

[Answer] C. Zhong Gong analysis: find the score of the fourth question. It is known that each question is 4 points more than the previous one. Then the score of each question is an equal difference. So the total score of 120 is equal to the middle term multiplied by half the number of terms. The sum of the fourth and fifth terms is 120/4 = 30, the tolerance is 4, and the fourth term is equal to (30-4) / 2 = 13. , Choose C.

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(Responsible editor: Zhang Ye)

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