ARDI\u015eIK SAYILAR<\/p>\n
Belli bir kurala g\u00f6re bir birini takip eden say\u0131 gruplar\u0131na ard\u0131\u015f\u0131k say\u0131lar denir.<\/p>\n
Ard\u0131\u015f\u0131k do\u011fal say\u0131lar; 0, 1, 2, 3, 4, 5, \u2026….<\/p>\n
Ard\u0131\u015f\u0131k tek say\u0131lar; 1, 3, 5, 7, 9, 11, 13, 15, \u2026……<\/p>\n
Ard\u0131\u015f\u0131k \u00e7ift say\u0131lar; 0, 2, 4, 6, 8, 10, 12, 14, 16, \u2026……<\/p>\n
4 \u00fcn kat\u0131 olan ard\u0131\u015f\u0131k do\u011fal say\u0131lar; 0, 4, 8, 12, 16, \u2026….. \u015feklinde devam eder.<\/p>\n
<\/p>\n
n bir tam say\u0131 olmak \u00fczere,<\/p>\n
<\/p>\n
1- Ard\u0131\u015f\u0131k d\u00f6rt tam say\u0131 s\u0131ras\u0131yla;<\/p>\n
<\/p>\n
n, n + 1, n + 2, n + 3 t\u00fcr.<\/p>\n
<\/p>\n
2-Ard\u0131\u015f\u0131k d\u00f6rt \u00e7ift say\u0131 s\u0131ras\u0131yla;<\/p>\n
<\/p>\n
2n, 2n + 2, 2n + 4, 2n + 6 d\u0131r.<\/p>\n
<\/p>\n
3-Ard\u0131\u015f\u0131k d\u00f6rt tek say\u0131 s\u0131ras\u0131yla;<\/p>\n
<\/p>\n
2n + 1, 2n + 3, 2n + 5, 2n + 7 dir.<\/p>\n
<\/p>\n
4-\u00dc\u00e7\u00fcn kat\u0131 olan ard\u0131\u015f\u0131k d\u00f6rt tam say\u0131 s\u0131ras\u0131yla;<\/p>\n
<\/p>\n
3n, 3n + 3, 3n + 6, 3n + 9 dur.<\/p>\n
<\/p>\n
Ard\u0131\u015f\u0131k say\u0131lar\u0131n toplam\u0131, say\u0131 adedine b\u00f6l\u00fcn\u00fcrse ortanca terim bulunur. E\u011fer say\u0131 adedi \u00e7ift ise, ortanca terim say\u0131 dizisine ait de\u011fildir.<\/p>\n
<\/p>\n
<\/p>\n
UYARI : \u0130ki ard\u0131\u015f\u0131k say\u0131n\u0131n toplam\u0131 daima tektir. B\u00fct\u00fcn \u00e7ift say\u0131lar\u0131n toplam\u0131 daima \u00e7ifttir.<\/p>\n
<\/p>\n
Biraz \u00f6rnek \u00e7\u00f6zelim:<\/p>\n
<\/p>\n
SORU : \u0130ki ard\u0131\u015f\u0131k say\u0131n\u0131n toplam\u0131 97 ise bu say\u0131lar ka\u00e7t\u0131r?<\/p>\n
<\/p>\n
Cevap : n<\/p>\n
<\/p>\n
+ n + 1<\/p>\n
<\/p>\n
97<\/p>\n
<\/p>\n
Yukar\u0131da iki ard\u0131\u015f\u0131k say\u0131 n ve n +1 ile g\u00f6sterilmi\u015ftir. \u0130lk i\u015f olarak fazlal\u0131k olan 1 i toplamdan yani 97 den \u00e7\u0131kar\u0131yoruz.<\/p>\n
<\/p>\n
97 \u2013 1 = 96<\/p>\n
<\/p>\n
Art\u0131k fazlal\u0131k kalmad\u0131\u011f\u0131na g\u00f6re; ve iki ard\u0131\u015f\u0131k say\u0131m\u0131z oldu\u011funa g\u00f6re, kalan say\u0131y\u0131 ikiye b\u00f6lerek k\u00fc\u00e7\u00fck say\u0131y\u0131 bulabiliriz.<\/p>\n
<\/p>\n
96 : 2 = 48 K\u00fc\u00e7\u00fck say\u0131 B\u00fcy\u00fck say\u0131y\u0131 bulmak i\u00e7in ise; 48 + 1 = 49<\/p>\n
<\/p>\n
<\/p>\n
<\/p>\n
SORU : \u0130ki ard\u0131\u015f\u0131k \u00e7ift say\u0131n\u0131n toplam\u0131 178 ise bu say\u0131lar ka\u00e7t\u0131r?<\/p>\n
<\/p>\n
Cevap : n<\/p>\n
<\/p>\n
+ n + 2<\/p>\n
<\/p>\n
178<\/p>\n
<\/p>\n
Ard\u0131\u015f\u0131k \u00e7ift say\u0131lar\u0131n iki\u015fer iki\u015fer art\u0131yor olmas\u0131 sebebiyle, bu defa ikinci say\u0131m\u0131zdaki 2 fazlal\u0131\u011f\u0131n\u0131 toplamdan \u00e7\u0131kar\u0131yoruz.<\/p>\n
<\/p>\n
178 \u2013 2 = 176<\/p>\n
<\/p>\n
Art\u0131k fazlal\u0131k kalmad\u0131. iki say\u0131m\u0131z oldu\u011fu i\u00e7in sonucu ikiye b\u00f6lerek k\u00fc\u00e7\u00fck say\u0131m\u0131z\u0131 bulabiliriz.<\/p>\n
<\/p>\n
176 : 2 = 88 K\u00fc\u00e7\u00fck say\u0131<\/p>\n
<\/p>\n
B\u00fcy\u00fck say\u0131, k\u00fc\u00e7\u00fck say\u0131dan 2 fazla oldu\u011funa g\u00f6re; 2 ekleyerek b\u00fcy\u00fck say\u0131y\u0131 bulabiliriz.<\/p>\n
<\/p>\n
88 + 2 = 90 B\u00fcy\u00fck say\u0131<\/p>\n
<\/p>\n
NOT : Bir \u00e7ok \u00f6\u011frencimizin d\u00fc\u015ft\u00fc\u011f\u00fc tuzak; verilen say\u0131y\u0131 hemen say\u0131 adedine b\u00f6lmeleridir. Unutmayal\u0131m ki; ard\u0131\u015f\u0131k say\u0131lar belirli oranlarda artarak gider. Sizlerin \u00f6ncelikle bu art\u0131\u015f\u0131 toplamdan \u00e7\u0131karman\u0131z gerekir. Daha sonra ka\u00e7 say\u0131 varsa, ona g\u00f6re b\u00f6lme i\u015flemini yaparak k\u00fc\u00e7\u00fck say\u0131m\u0131z\u0131 bulabiliriz. Bu b\u00f6lme i\u015flemi sonras\u0131 \u00e7\u0131kan sonu\u00e7 b\u00fct\u00fcn i\u015flemlerde k\u00fc\u00e7\u00fck say\u0131d\u0131r. B\u00fcy\u00fck say\u0131y\u0131 bulmak i\u00e7in ise tekrar ekleme yapman\u0131z gerekmektedir.<\/p>\n
<\/p>\n
Yukar\u0131da da de\u011finildi\u011fi \u00fczere bu art\u0131\u015f; ard\u0131\u015f\u0131k say\u0131larda 1, ard\u0131\u015f\u0131k \u00e7ift ve ard\u0131\u015f\u0131k tek say\u0131larda 2’dir.<\/p>\n
<\/p>\n
Ard\u0131\u015f\u0131k \u00e7ift ve ard\u0131\u015f\u0131k tek say\u0131larla ilgili problemler ayn\u0131 \u015fekilde \u00e7\u00f6z\u00fcl\u00fcr. \u00e7ift ve tek olu\u015flar\u0131 kafan\u0131z\u0131 kar\u0131\u015ft\u0131rmas\u0131n. \u00c7\u00fcnk\u00fc her ikisi de 2’\u015fer 2’\u015fer artmaktad\u0131r. Bir tane de tek say\u0131larla ilgili \u00e7\u00f6zerek g\u00f6relim.<\/p>\n
<\/p>\n
SORU : Ard\u0131\u015f\u0131k iki tek say\u0131n\u0131n toplam\u0131 108’dir. Buna g\u00f6re k\u00fc\u00e7\u00fck ve b\u00fcy\u00fck say\u0131lar\u0131 bulal\u0131m.<\/p>\n
<\/p>\n
Cevap : n<\/p>\n
<\/p>\n
+ n + 2<\/p>\n
<\/p>\n
108<\/p>\n
<\/p>\n
Yine \u00f6ncelikli hedefimiz fazlal\u0131\u011f\u0131 \u00e7\u0131karmak,<\/p>\n
<\/p>\n
108 – 2 = 106<\/p>\n
<\/p>\n
Daha sonra iki say\u0131 oldu\u011fu i\u00e7in sonucu ikiye b\u00f6lerek k\u00fc\u00e7\u00fck say\u0131y\u0131 bulmak,<\/p>\n
<\/p>\n
106 \/ 2 = 53 K\u00fc\u00e7\u00fck say\u0131<\/p>\n
<\/p>\n
B\u00fcy\u00fck say\u0131 i\u00e7in ise 2’yi tekrar eklememiz yeterli,<\/p>\n
<\/p>\n
53 + 2 = 55 B\u00fcy\u00fck say\u0131<\/p>\n
<\/p>\n
<\/p>\n
<\/p>\n
ISINMA TURLARI SONA ERD\u0130, SORULARIMIZI B\u0130RAZ DAHA ZORLA\u015eTIRALIM… \ud83d\ude42<\/p>\n
<\/p>\n
SORU: Ard\u0131\u015f\u0131k \u00fc\u00e7 say\u0131n\u0131n toplam\u0131 246’d\u0131r. Buna g\u00f6re k\u00fc\u00e7\u00fck, orta ve b\u00fcy\u00fck say\u0131lar\u0131 bulunuz.<\/p>\n
<\/p>\n
Cevap: n<\/p>\n
<\/p>\n
n + 1<\/p>\n
<\/p>\n
+ n + 2<\/p>\n
<\/p>\n
246<\/p>\n
<\/p>\n
bu defaki fazlal\u0131klar\u0131m\u0131z 1 ve 2 —— yani 1 + 2 = 3<\/p>\n
<\/p>\n
Bu fazlal\u0131\u011f\u0131 toplamdan \u00e7\u0131karal\u0131m<\/p>\n
<\/p>\n
246 – 3 = 243<\/p>\n
<\/p>\n
Bu defa iki de\u011fil, \u00fc\u00e7 say\u0131m\u0131z var. O halde sonucuda 3’e b\u00f6lmemiz gerekiyor.<\/p>\n
<\/p>\n
243 \/ 3 = 81 K\u00fc\u00e7\u00fck say\u0131<\/p>\n
<\/p>\n
Ortanca say\u0131 k\u00fc\u00e7\u00fck say\u0131dan 1 fazla oldu\u011funa g\u00f6re;<\/p>\n
<\/p>\n
81 + 1 = 82 ortanca say\u0131<\/p>\n
<\/p>\n
B\u00fcy\u00fck say\u0131 k\u00fc\u00e7\u00fck say\u0131dan 2 fazla oldu\u011funa g\u00f6re;<\/p>\n
<\/p>\n
81 + 2 = 83 B\u00fcy\u00fck say\u0131d\u0131r<\/p>\n
<\/p>\n
SORU: Ard\u0131\u015f\u0131k \u00fc\u00e7 \u00e7ift say\u0131n\u0131n toplam\u0131 222’dir. Buna g\u00f6re; k\u00fc\u00e7\u00fck, ortanca ve b\u00fcy\u00fck say\u0131lar\u0131 bulunuz.<\/p>\n
<\/p>\n
\u00c7\u00f6z\u00fcm: \u00c7ift say\u0131lar 2’\u015fer 2’\u015fer artmaktayd\u0131. O halde;<\/p>\n
<\/p>\n
n<\/p>\n
<\/p>\n
n + 2<\/p>\n
<\/p>\n
+ n + 4<\/p>\n
<\/p>\n
222<\/p>\n
<\/p>\n
Fazlal\u0131klar\u0131m\u0131z 2 ve 4 —– Yani 2 + 4 = 6<\/p>\n
<\/p>\n
Bu fazlal\u0131\u011f\u0131 \u00e7\u0131karal\u0131m 222 – 6 = 216<\/p>\n
<\/p>\n
\u00dc\u00e7 say\u0131m\u0131z oldu\u011fu i\u00e7in yine 3’e b\u00f6lelim ve k\u00fc\u00e7\u00fck say\u0131m\u0131z\u0131 bulal\u0131m.<\/p>\n
<\/p>\n
216 \/ 3 = 72 K\u00fc\u00e7\u00fck say\u0131<\/p>\n
<\/p>\n
72 + 2 = 74 Ortanca say\u0131<\/p>\n
<\/p>\n
72 + 4 = 76 B\u00fcy\u00fck say\u0131<\/p>\n
<\/p>\n
<\/p>\n
<\/p>\n
SORU: Ard\u0131\u015f\u0131k d\u00f6rt say\u0131n\u0131n toplam\u0131 418′ dir. Buna g\u00f6re bu say\u0131lar\u0131 bulunuz.<\/p>\n
<\/p>\n
Cevap: 1.say\u0131 n<\/p>\n
<\/p>\n
2.say\u0131 n + 1<\/p>\n
<\/p>\n
3.say\u0131 n + 2<\/p>\n
<\/p>\n
4.say\u0131 + n + 3<\/p>\n
<\/p>\n
418<\/p>\n
<\/p>\n
D\u00f6rt say\u0131m\u0131zda yukar\u0131da belirtilmi\u015ftir. fazlal\u0131klara bakt\u0131\u011f\u0131m\u0131zda; 1, 2 ve 3′ \u00fc g\u00f6r\u00fcyoruz. yani 1 + 2 + 3 = 6<\/p>\n
<\/p>\n
Fazlal\u0131\u011f\u0131m\u0131z\u0131 \u00e7\u0131kar\u0131yoruz, 418 – 6 = 412<\/p>\n
<\/p>\n
D\u00f6rt say\u0131m\u0131z oldu\u011fu i\u00e7in sonucu 4’e b\u00f6lerek k\u00fc\u00e7\u00fck say\u0131m\u0131z\u0131 yani 1.say\u0131m\u0131z\u0131 buluyoruz.<\/p>\n
<\/p>\n
412 \/ 4 = 103 (1.say\u0131)<\/p>\n
<\/p>\n
103 + 1 = 104 (2.say\u0131)<\/p>\n
<\/p>\n
103 + 2 = 105 (3.say\u0131)<\/p>\n
<\/p>\n
103 + 3 = 106 (4.say\u0131)<\/p>\n","protected":false},"excerpt":{"rendered":"
ARDI\u015eIK SAYILAR Belli bir kurala g\u00f6re bir birini takip eden say\u0131 gruplar\u0131na ard\u0131\u015f\u0131k say\u0131lar denir. Ard\u0131\u015f\u0131k do\u011fal say\u0131lar; 0, 1, 2, 3, 4, 5, \u2026…. Ard\u0131\u015f\u0131k tek say\u0131lar; 1, 3, 5, 7, 9, 11, 13, 15, \u2026…… Ard\u0131\u015f\u0131k \u00e7ift say\u0131lar; 0, 2, 4, 6, 8, 10, 12, 14, 16, \u2026…… 4 \u00fcn kat\u0131 olan ard\u0131\u015f\u0131k … Devam\u0131n\u0131 oku…<\/a><\/p>\n","protected":false},"author":1685,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[13917,13918,13919],"class_list":["post-39654","post","type-post","status-publish","format-standard","hentry","category-mt","tag-ardisik-sayilar","tag-ardisik-sayilar-ders-notlari","tag-matematik-ders-notu"],"_links":{"self":[{"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/posts\/39654","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/users\/1685"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/comments?post=39654"}],"version-history":[{"count":0,"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/posts\/39654\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/media?parent=39654"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/categories?post=39654"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sorubak.com\/blog\/wp-json\/wp\/v2\/tags?post=39654"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}