CAPITULO XXXVII
Progresiones
Progresiones
- Ejercicio 288
Hallar la suma de los:
- 8 primeros términos de
÷ 15.19.23…..
Sea : a=15,n=8,r=19–15=4 u =a+( n–1 ) r u =15+( 8–1 ) 4 u =15+7( 4 ) u =15+28 u =43 S = ( a+u ) n 2 S = ( 15+43 ) 2 S =( 58 ) 4 S =232 - 19 primeros términos de
÷ 31.38.45…..
Sea : a=31,n=19,r=38–31=7 u =a+( n–1 ) r u =31+( 19–1 ) 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 - 24 primeros términos de
÷ 42.32.22…..
Sea : a=42,n=24,r=32–42=–10 u =a+( n–1 ) r u =42+( 24–1 ) ( –10 ) u =42+( 23 ) ( –10 ) u =42–230 u =–188 S = ( a+u ) n 2 S = ( 42–188 ) 2 S =( –146 ) 12 S =–1752 - 80 primeros términos de
÷ –10.–6.–2…..
Sea : a=–10,n=80,r=–6+10=4 u =a+( n–1 ) r u =–10+( 80–1 ) 4 u =–10+( 79 ) 4 u =–10+316 u =306 S = ( a+u ) n 2 S = ( –10+306 ) 2 S =( 296 ) 40 S =11840 - 60 primeros términos de
÷ 11.1.–9…..
Sea : a=11,n=60,r=1–11=–10 u =a+( n–1 ) r u =11+( 60–1 ) ( –10 ) u =11+( 59 ) ( –10 ) u =11–590 u =–579 S = ( a+u ) n 2 S = ( 11–579 ) 2 S =( –568 ) 30 S =–17040 - 50 primeros términos de
÷ –5.–13.–21…..
Sea : a=–5,n=50,r=–13+5=–8 u =a+( n–1 ) r u =–5+( 50–1 ) ( –8 ) u =–5+( 49 ) ( –8 ) u =–5–392 u =–397 S = ( a+u ) n 2 S = ( –5–397 ) 2 S =( –402 ) 25 S =–10050 - 9 primeros términos de
÷
1
2
.1.
3
2
…..
Sea : a= 1 2 ,n=9,r=1– 1 2 = 1 2 u =a+( n–1 ) r u = 1 2 +( 9–1 ) ( 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 - 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+( n–1 ) r u = 3 10 +( 14–1 ) ( 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 - 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+( n–1 ) r u = 3 4 +( 19–1 ) ( 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 - 34 primeros términos de
÷
2
5
.
7
55
…..
Sea : a= 2 5 ,n=34,r= 7 55 – 2 5 =– 3 11 u =a+( n–1 ) r u = 2 5 +( 34–1 ) ( – 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 primeros términos de
÷ 2
1
3
.3
2
15
…..
Sea : a= 7 3 ,n=11,r= 47 15 – 7 3 = 4 5 u =a+( n–1 ) r u = 7 3 +( 11–1 ) ( 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 - 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+( n–1 ) r u = 13 4 +( 46–1 ) ( 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 - 17 primeros términos de
÷ –2.
1
4
……
Sea : a=–2,n=17,r= 1 4 +2= 9 4 u =a+( n–1 ) r u =–2+( 17–1 ) ( 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 - 12 primeros términos de
÷ –5.–4
5
8
……
Sea : a=–5,n=12,r=– 37 8 +5= 3 8 u =a+( n–1 ) r u =–5+( 12–1 ) ( 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