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数学 中学生

2023 市川高等学校 数学 (3)の詳しい解説をお願いします。

13 X. Yの2人が次の問題の解き方を相談しながら考え ている。 n番目に 4n-5 が書かれている数の列Aと, 7番目に n2-2n-1 が書かれている数の列Bがある。 ただし, nは自然数とする。 A,B を書き並べると, A: -1, 3,7, 11, 15, B: -2, -1,2,7, 14, A. Bに現れる数字を小さい順に並べた数の列をCとす るとき, 2023はCの中で何番目に現れるか。 X : 途中過程を書きやすいように, A. Bの番目の数を それぞれ an, b, と表すことにしよう。 Y : 例えばAの3番目の数は a3 で, 計算は4n-5に n=3 を代入した7になるから,a3=7と書けばいい んだね。 同じようにBの10番目の数を求めると, b10=アとなるね。 X : では, A,Bの規則性を見てみよう。 Aは an=4n-5 だから最初の -1 から4ずつ増えていく ことと,奇数しか現れないことがわかるけど, B はど うだろうか。 Y:bm=n²-2-1 だけど規則が読み取りにくいね。 規 則を見つけるために隣り合う数の差をとってみようか。 (n+1) 番目の数からn番目の数を引いてみよう。 X: b = n2-2n-1 だから bn+1-bn={(n+1)2-2(n+1)-1}-(n2-2n-1) =2n-1 となるね。 Y : ということは, 隣り合う数の差が必ず奇数だからBは 偶数から始まって偶数と奇数が交互に現れるね。 だけ ど,これだけではまだ特徴がわからないな。 X : そうしたら次はもう1つ離れた数との差をとってみよ うよ。 (n+2) 番目の数からn番目の数を引いてみよう。 Y: bn+2 -b を計算するとイ となるね。 X : わかった。 これと今までわかっている特徴を合わせる と問題が解けるね。 (1) ア イにあてはまる式や値を答えよ。 (2) Bの数の列において, 2023が何番目か求めよ。 (3) Cの数の列において, 2023が何番目か求めよ。 問題↓解説↑ 3 (1)(イ) bn+2=(n+2)-2(n+2)-1 =n2+2n-1より, bn+2-6m=n2+2n-1- (n2-2n - 1) = 4n (2) n2-2n-1=2023 (n+44)(n-46) = 0 n>0より, n = 46 (3)4n5= 2023 n= ¥507 より, Aの列において, 2023は507番目の数である。 Cの数の列において 2023までの数の個数は, A の数の 列における 2023 までの数の個数と、Bの数の列における 2023 までの数の個数の和からAの数の列とBの数の列に 共通する2023 を含めた数の個数を引けばよい。 A の数の 列とBの数の列に共通する数の列Dを書き並べると, D: -1, 7,23,47, ...... DはBの偶数番目の数が並んでいるから, n番目の数を dn とすると, dn=bzn=(2n)2-2 × 2n-1=4n²-4n-1 4n²-4n-1=2023 n2-n-506 = 0 >0より, n=23 (n+22) (n-23) = 0 よって, Cの数の列において, 2023 は, |507 +46-23530 ( 番目)

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英語 中学生

③はat first になるんですけどどうやってとけばいいんでしょうか?なにか方法があれば教えて欲しいです

結化(Yuka), リリ 九里(M. Greenの英語の授業で発表を行いました。 発表を聞いたクリー ン先生は, 結花さんの発表についてコメントを書きました。 【 結花さんの発表】 【グリーン先生のコメント を読んで,後の1から8までの各問いに答えなさい。 sog vin 【結花さんの発表】 He Many people in Shiga have worked as volunteers. My grandfather is one of them. worked as a junior high school math teacher for many years and retired five years ago. He has worked as a volunteer at the community center since then. Many children go there to play and study together after school and on weekends. He helps them ( 1 ) every day. He always says that working for other people makes him happy. His words made me interested in volunteer work. bon OR I became a high school student and wanted to try something new. So I did volunteer work at the community center this summer. Now, I will talk about my experiences. I hope my speech will give you a chance to think about volunteer work. During summer vacation, I visited the community center. The community center 【used / many /is/ people/byl living in my city. And the volunteers do a variety of work. My first volunteer work was to take care of elderly people. I played some games and talked with them in the morning. Mr. Sato, one of the elderly men, said to me, "I had a good time today. I live alone and don't have so many chances to talk to other people, especially to young people like you. So I enjoyed talking with you." I was happy to hear that. In the afternoon, I saw a little foreign girl in the playroom. She was drawing a picture alone. ), I hesitated to talk to her because of my English. Then I remembered Mr. Sato's words. So I went to the girl and said, "Hi, I'm Yuka. You are good at drawing pictures. [4]" She smiled and showed me her picture. Then she said, "I will give this picture to my Japanese friend for her birthday. I want to write 'Happy Birthday!' in Japanese on the picture. Can you teach me how to write it?" I was glad to hear that. I taught her how to write it in hiragana. She practiced many times and looked very happy when she saw the picture after she finally finished 5[write] her message in Japanese. Then she said to me, "Thank you for helping me!" Her big smile made me very happy. These experiences reminded me of my grandfather's words. Before doing volunteer work, I thought that helping other people was to make them happy. However, I realized that helping other people made me happy,) too. So we can [ 6 ]. Now I'm looking forward to doing volunteer work again during spring vacation. Thank you for listening. (注) volunteer(s): ボランティアをする人 retire: 退職する community center: E play : 遊ぶ hesitate : ためらう chance : playroom: 【グリーン先生のコメント】 Your speech was great. I'm glad that you learned an important thing. I do volunteer work, too. I visit the city library every Saturday. I help foreign people there. Some foreign people don't understand Japanese. So I help them borrow books. Do you like to read books? The staff members are looking for someone who can read books to children. If you are interested, why don't we visit it together this Saturday?

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