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CAPITULO XXXVII

Progresiones
Ejercicio 288
Hallar la suma de los:
  1. 8 primeros términos de ÷ 15.19.23…..
    Sea : a=15,n=8,r=1915=4 u =a+(n1 ) r u =15+(81 ) 4 u =15+7( 4 ) u =15+28 u =43 S = (a+u ) n 2 S = (15+43 ) 2 S =( 58 ) 4 S =232
  2. 19 primeros términos de ÷ 31.38.45…..
    Sea : a=31,n=19,r=3831=7 u =a+(n1 ) r u =31+(191 ) 7 u =31+18( 7 ) u =31+126 u =157 S = (a+u ) n 2 S = (31+157 ) 19 2 S = 19 2 S =1786
  3. 24 primeros términos de ÷ 42.32.22…..
    Sea : a=42,n=24,r=3242=10 u =a+(n1 ) r u =42+(241 ) (10 ) u =42+( 23 ) (10 ) u =42230 u =188 S = (a+u ) n 2 S = (42188 ) 2 S =(146 ) 12 S =1752
  4. 80 primeros términos de ÷ 10.6.2…..
    Sea : a=10,n=80,r=6+10=4 u =a+(n1 ) r u =10+(801 ) 4 u =10+( 79 ) 4 u =10+316 u =306 S = (a+u ) n 2 S = (10+306 ) 2 S =( 296 ) 40 S =11840
  5. 60 primeros términos de ÷ 11.1.9…..
    Sea : a=11,n=60,r=111=10 u =a+(n1 ) r u =11+(601 ) (10 ) u =11+( 59 ) (10 ) u =11590 u =579 S = (a+u ) n 2 S = (11579 ) 2 S =(568 ) 30 S =17040
  6. 50 primeros términos de ÷ 5.13.21…..
    Sea : a=5,n=50,r=13+5=8 u =a+(n1 ) r u =5+(501 ) (8 ) u =5+( 49 ) (8 ) u =5392 u =397 S = (a+u ) n 2 S = (5397 ) 2 S =(402 ) 25 S =10050
  7. 9 primeros términos de ÷ 1 2 .1. 3 2 …..
    Sea : a= 1 2 ,n=9,r=1 1 2 = 1 2 u =a+(n1 ) r u = 1 2 +(91 ) ( 1 2 ) u = 1 2 +() ( 1 2 ) u = 1 2 +4 u = 9 2 S = (a+u ) n 2 S = ( 1 2 + 9 2 ) 9 2 S = ( 2 ) 9 2 S = 45 2 22 1 2
  8. 14 primeros términos de ÷ 3 10 . 2 5 . 1 2 …..
    Sea : a= 3 10 ,n=14,r= 2 5 3 10 = 1 10 u =a+(n1 ) r u = 3 10 +(141 ) ( 1 10 ) u = 3 10 +( 13 ) ( 1 10 ) u = 3 10 + 13 10 u = u = 8 5 S = (a+u ) n 2 S = ( 3 10 + 8 5 ) 2 S =( 19 10 ) 7 S = 133 10 13 3 10
  9. 19 primeros términos de ÷ 3 4 . 3 2 . 9 4 …..
    Sea : a= 3 4 ,n=19,r= 3 2 3 4 = 3 4 u =a+(n1 ) r u = 3 4 +(191 ) ( 3 4 ) u = 3 4 +() ( 3 ) u = 3 4 + 27 2 u = 57 4 S = (a+u ) n 2 S = ( 3 4 + 57 4 ) 19 2 S = ( 4 ) 19 2 S = 15( 19 ) 2 S = 285 2 142 1 2
  10. 34 primeros términos de ÷ 2 5 . 7 55 …..
    Sea : a= 2 5 ,n=34,r= 7 55 2 5 = 3 11 u =a+(n1 ) r u = 2 5 +(341 ) ( 3 11 ) u = 2 5 +() ( 3 11 ) u = 2 5 9 u = 43 5 S = (a+u ) n 2 S = ( 2 5 43 5 ) 2 S =( 41 5 ) 17 S = 697 5 139 2 5
  11. 11 primeros términos de ÷ 2 1 3 .3 2 15 …..
    Sea : a= 7 3 ,n=11,r= 47 15 7 3 = 4 5 u =a+(n1 ) r u = 7 3 +(111 ) ( 4 5 ) u = 7 3 +() ( 4 5 ) u = 7 3 +8 u = 31 3 S = (a+u ) n 2 S = ( 7 3 + 31 3 ) 11 2 S = ( 3 ) 11 2 S =( 19 3 ) 11 S = 209 3 69 2 3
  12. 46 primeros términos de ÷ 3 1 4 .3 13 20 ……
    Sea : a= 13 4 ,n=46,r= 73 20 13 4 = 2 5 u =a+(n1 ) r u = 13 4 +(461 ) ( 2 5 ) u = 13 4 +() ( 2 5 ) u = 13 4 +18 u = 85 4 S = (a+u ) n 2 S = ( 13 4 + 85 4 ) 3 S =( ) 23 S = 1127 2 563 1 2
  13. 17 primeros términos de ÷ 2. 1 4 ……
    Sea : a=2,n=17,r= 1 4 +2= 9 4 u =a+(n1 ) r u =2+(171 ) ( 9 4 ) u =2+() ( 9 4 ) u =2+36 u =34 S = (a+u ) n 2 S = (2+34 ) 17 2 S = ( 17 ) 2 S =272
  14. 12 primeros términos de ÷ 5.4 5 8 ……
    Sea : a=5,n=12,r= 37 8 +5= 3 8 u =a+(n1 ) r u =5+(121 ) ( 3 8 ) u =5+( 11 ) ( 3 8 ) u =5+ 33 8 u = 7 8 S = (a+u ) n 2 S = (5 7 8 ) 2 S =( 47 ) S = 141 4 35 1 4