May2026Q7

追加: 2026-05-14

[00:00:02]All right. So, question number seven.

[00:00:04]Question number seven says, "The diagram below shows part of a number chart. The numbers on the chart follow various patterns. Study the pattern pattern of numbers and answer the questions that follow. All right. So, looking at the pattern, we can see that each set of numbers is going up by seven.

[00:00:26]So the um for column one the um the general term would be um 7 r plus no it's just 7 r so the general term here would be 7 r where r is the term number Um for the second one it's going to be 7 R + 2 and the next one is going to be 7 R. 7 * 1 is 7. What must I add to 7 to get 11?

[00:01:09]That is 4.

[00:01:11]What number should be placed in column 9? Column one, row 9. So in column one um C1 R9 we're going to have um R the row number which is R is 9. So this is 7 * 9 this is 63.

[00:01:39]Now the following diagram um represents a given row from the chart described on page 22.

[00:01:48]All right.

[00:01:50]Fill in the three missing um the three missing well let's call the row number x.

[00:02:02]So the row number is x.

[00:02:04]Um now for column 2 the ter sorry the general term is 7 r + 2 7 r + 2.

[00:02:15]So this would be 7 x + 2 is equal to 63.

[00:02:26]So 7 x will be 653 - 2. 7 x is 6 51.

[00:02:37]Divide both sides by 7 and we get x is equal to 93.

[00:02:52]So the value here is 93.

[00:02:55]Then the next one is going to be 7 * 93.

[00:02:58]So 93 * 7 this is 621 and the last column is 7 R + 4 so it's 7 * 93 so 7 * 93 + 4 so this is um 650 55.

[00:03:29]All right, I probably didn't have to do all of this just to get the answer, but I have the answers. Um, which row would contain um the number 942?

[00:03:43]Explain how you arrived at your answer.

[00:03:48]Row, the row that contains the number um 792.

[00:03:54]So it would have to be either 7 x 7 * r row number is equal to 942 r is equal to 942 / 7.

[00:04:19]So 942 / by 7 and that's a decimal. So um 942 does not belong to um 942 / 7.

[00:04:37]So this is a decimal.

[00:04:41]So it does not belong 942 does not belong in column one.

[00:04:48]Um 7 R + 2 is equal to 942.

[00:04:58]7R would be equal to 942 / - 2.

[00:05:07]So R would be what? 940 / 7.

[00:05:19]All right, this is also a decimal. So I'm just double checking. Yeah, 940 / 7. It's a decimal. So it does not belong in all right doesn't belong in column 2.

[00:05:41]7 R + 4 is = 942.

[00:05:47]So 7 R is 942 - 4 which is 938.

[00:05:59]Divide both sides by 7 we get R 938ide by 7.

[00:06:07]So this is equal to 134.

[00:06:12]So the question is asked um the row number explain your how you arrive at your answer. The row number is 134.

[00:06:24]Explanation well um what I did is I divided I used The general term to calculate the row number for um assuming that um 9 42 is a um number in um in um one of the three columns.

[00:07:53]Um the um general term the column the general That gives a whole number value.

[00:08:25]for the row number is the column the um is the column 9 42 is in.

[00:08:52]All right, let's see what comes next.

[00:08:55]The B part of the question says, a sequence is formed using the diagram made up of um equ um equilateral triangles each um constructed from sticks of units length. The first four diagrams in the sequence are shown. The table below shows the relationship among the number of equilateral triangles. E the number of sticks that form in each diagrams.

[00:09:25]S the number of dots. D the number of dots. D.

[00:09:32]Um study the pattern of numbers in each row of the table and answer the questions that follow. Right? So this is going up by two.

[00:09:42]General term is ur is um 2 r - 1.

[00:09:52]This is going up by 4.

[00:09:55]The general term ur is 4 r - 1. This is going up by 2.

[00:10:07]The general term ur is 2 r + 1.

[00:10:14]This is going to be 2 n -1 4 n - 1 and 2 n + 1.

[00:10:28]Complete the rows in the table that corresponds to diagram diagram 9. Using your answer is in B I show that the difference between the number of um equilateral triangles and the number of dots is always equal to two. So the number of difference between the number of equilateral triangle and the number of dots is 2 n + 1 - 2 n - 1.

[00:11:13]And this is 2 n + 1 - 2 n + 1. This is 2 n - 2 n + 1 + 1. The difference is 2. And that is the end of the question.