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Mathematics Senior High

最後の黒線で引いたところの計算が分かりません。

00000 基本例題 126 連立漸化式 (2) 数列{an}, {bn}をa=1, b,=-1, an+1=54-4b, bn+1=an+bnで定めるとき (1) an+1+xbx+1=y(an+xb²)を満たすx,yの値を求めよ。 (2) 数列{an}, {bn}の一般項を求めよ。 指針 p.575 基本例題 125 (1) と同様に, 〔解法1] 「等比数列を利用」の方針によって解けばよい。 an+xb.=(a+xbi)y (2) (1) から 数列 (an+xb.) は公比yの等比数列となり これに α = bats-b を代入し, an を消去すると bn+1=(1-x) b.+ (②2+xbi)y"-1 ① += pa.+α型の化式 (p.564 基本例題118) に帰着。・・・・・... よって, ① の両辺をy"+ で割ればよい。 解答 (1) an+1+xbn+1=5an-4bn+x(an+bn) =(5+x)an+(-4+x)bn よって, an+1+xbn+1 = y (an+xbm) とすると (5+x)an+(-4+x)bm=yan+xybn これがすべてのnについて成り立つための条件は 5+x=y, -4+x=xy 5+x=yを4+x=xy に代入して整理すると x2+4x+4=0 ゆえに x=-2 したがって 求めるx, yの値は (2) (1) から これに α = bn+1- 6m を代入すると bn+1=36+3 an-2bm=3.3"-1 = 3" すなわちa=26+3 & HA ***** an+1=b+2-bati これらを①に代入して bn+2-6b+1+9bn=0 特性方程式 解くとx=3 (重解) an+1-2bn+1=3(an-2bn) よって, p.573 基本例題124 よって, 数列{an-26 ) は,初項α-26, 3, 公比3の等比 と同じ方針で、 まず一般項b 数列であるから月 を求める。 x=-2, y=3 3¹ bn 3" bn+1 bn 1 3+1 3" 3 両辺を 3 +1 で割ると b₁ 数列{2}は,初項 12/1=11/11/13 公差 1/1/3の等差数列で =. + あるから --1/3+(n-1)-1-12 . よって 基本118,125 an=3"-¹(2n-1), b=3"-¹(n-2) [[解法2] [1つの数列 に関する漸化式に帰着させ る] の方針による解答 an+1=5an-4bx bsity=ax+bn ② から an=b+1-bs. ****** ② 6x+9= 0 を 44,00 Jr! <an+1=pan+g型は両辺を g" +1 で割る(p.564 参照)。 a=26+3" に代入 (基 1

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English Senior High

分かる方宜しくお願いします。

4 Reading Read the following passage and answer the questions. India has one of the oldest and largest film industries in the world. Graph 1 shows that, when it comes to the number of films made a year, India comes first, producing easily more films than the U.S. This has put the Indian city *Mumbai in the center of the global film industry. 2000 LESSON [Graph 1] Film Production (2015) 1500 5 One of the most common features of Indian films is that they have a lot of singing and dancing scenes. Songs often comment on the action taking place in the film. A song may be part of the *plot, so a character has a reason to sing. It may express a character's thoughts, or an event in the film, such as two characters falling in love. Some say that the reason for so much singing and dancing is because India is a 1o *multi-lingual country. Many different languages are spoken in India. As shown in Graph 2, by far the most common is *Hindi, which is used by nearly half of the population. Hindi is followed by *Bengali, *Telugu and many others. However, most people can enjoy the singing and dancing scenes, even if they don't understand the language spoken in the film. quifi 15 Among the Indian films, there are films in Hindi, Bengali, *Tamil, and so on. The ones in Hindi are called "*Bollywood" films (named after “Hollywood”) and are gaining huge popularity in and outside of the country. Its films are watched throughout Southern Asia and across many areas in the world, reaching over 90 countries. Indian cinema has become a global power. LENGLASU 1000 500 時制 0 France Britain the States China Japan India Napq?! 2-4 * 1642 Hindi Marathi /100 [Graph 2] Speakers of Languages in India (2011) 20 * Mumbai: AVR plot (話) 筋 multi-lingual: 多言語の Bengali : ベンガル語 Telugu: テルグ語 Tamil : タミル語 Bollywood : ボリウッド ※本書では,アメリカ発音, イギリス発音, オーストラリア発音の音声を扱っています。 ファッ Reading の CDトラック番号の横にそれぞれを米・英・豪で示しています。 40 Bengali Telugu Tamil Others Hindi : ヒンディー語 (256 words)

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