CAPITULO XXXVII
Progresiones
Progresiones
- Ejercicio 286
Hallar el
- 9° término de
÷
7.10.13….
Sea : a=7,n=9,r=10–7=3 u =a+( n–1 ) r u =7+( 9–1 ) 3 u =7+8( 3 ) u =7+24 u =31 - 12° término de
÷
5.10.15….
Sea : a=5,n=12,r=10–5=5 u =a+( n–1 ) r u =5+( 12–1 ) 5 u =5+11( 5 ) u =5+55 u =60 - 48° término de
÷
9.12.15….
Sea : a=9,n=48,r=12–9=3 u =a+( n–1 ) r u =9+( 48–1 ) 3 u =9+47( 3 ) u =9+141 u =150 - 63° término de
÷
3.10.17….
Sea : a=3,n=63,r=10–3=7 u =a+( n–1 ) r u =3+( 63–1 ) 7 u =3+62( 7 ) u =3+434 u =437 - 12° término de
÷
11.6.1….
Sea : a=11,n=12,r=6–11=–5 u =a+( n–1 ) r u =11+( 12–1 ) ( –5 ) u =11+11( –5 ) u =11–55 u =–44 - 28° término de
÷
19.12.5….
Sea : a=19,n=28,r=12–19=–7 u =a+( n–1 ) r u =19+( 28–1 ) ( –7 ) u =19+27( –7 ) u =19–189 u =–170 - 13° término de
÷
3.-1.-5….
Sea : a=3,n=13,r=–1–3=–4 u =a+( n–1 ) r u =3+( 13–1 ) ( –4 ) u =3+12( –4 ) u =3–48 u =–45 - 54° término de
÷
8.0.-8….
Sea : a=8,n=54,r=0–8=–8 u =a+( n–1 ) r u =8+( 54–1 ) ( –8 ) u =8+53( –8 ) u =8–424 u =–416 - 31° término de
÷
-7.-3.1….
Sea : a=–7,n=31,r=–3–( –7 ) =4 u =a+( n–1 ) r u =–7+( 31–1 ) ( 4 ) u =–7+30( 4 ) u =–7+120 u =113 - 17° término de
÷
-8.2.12….
Sea : a=–8,n=17,r=2–( –8 ) =10 u =a+( n–1 ) r u =–8+( 17–1 ) ( 10 ) u =–8+16( 10 ) u =–8+160 u =152 - 12° término de
÷
1
2
.
3
4
.1…
Sea : a= 1 2 ,n=12,r= 3 4 – 1 2 = 1 4 u =a+( n–1 ) r u = 1 2 +( 12–1 ) ( 1 4 ) u = 1 2 +11( 1 4 ) u = 1 2 + 11 4 u = 13 4 ↔ 3 1 4 - 17° término de
÷
2
3
.
5
6
.1…
Sea : a= 2 3 ,n=17,r= 5 6 – 2 3 = 1 6 u =a+( n–1 ) r u = 2 3 +( 17–1 ) ( 1 6 ) u = 2 3 +16( 1 6 ) u = 2 3 + 8 3 u = 10 3 ↔ 3 1 3 - 25° término de
÷
3
8
.
11
24
…
Sea : a= 3 8 ,n=25,r= 11 24 – 3 8 = 1 12 u =a+( n–1 ) r u = 3 8 +( 25–1 ) ( 1 12 ) u = 3 8 +124( 1 12 ) u = 3 8 +2 u = 19 8 ↔ 2 3 8 - 19° término de
÷
1
3
.
7
8
….
Sea : a= 1 3 ,n=19,r= 7 8 – 1 3 = 13 24 u =a+( n–1 ) r u = 1 3 +( 19–1 ) ( 13 24 ) u = 1 3 +18( 13 24 ) u = 1 3 + 39 4 u = 121 12 ↔ 10 1 12 - 27° término de
÷ 3
1
2
.5
1
4
….
Sea : a=3 1 2 ,n=27,r=5 1 4 –3 1 2 = 7 4 u =a+( n–1 ) r u =3 1 2 +( 27–1 ) ( 7 4 ) u = 7 2 +26( 7 4 ) u = 7 2 + 91 2 u = 2 u =49 - 36° término de
÷
7
9
.
1
3
….
Sea : a= 7 9 ,n=36,r= 1 3 – 7 9 =– 4 9 u =a+( n–1 ) r u = 7 9 +( 36–1 ) ( – 4 9 ) u = 7 9 +35( – 4 9 ) u = 7 9 – 140 9 u =– 133 9 ↔ –14 7 9 - 15° término de
÷
2
7
.
1
8
….
Sea : a= 2 7 ,n=15,r= 1 8 – 2 7 =– 9 56 u =a+( n–1 ) r u = 2 7 +( 15–1 ) ( – 9 56 ) u = 2 7 +14( – 9 56 ) u = 2 7 – 9 4 u =– 55 28 ↔ –1 27 28 - 21° término de
÷ –
3
5
.–
14
15
….
Sea : a=– 3 5 ,n=21,r=– 14 15 + 3 5 =– 1 3 u =a+( n–1 ) r u =– 3 5 +( 21–1 ) ( – 1 3 ) u =– 3 5 +20( – 1 3 ) u =– 3 5 – 20 3 u =– 109 15 ↔ –7 4 15 - 13° término de
÷ –
1
4
.–2
1
4
….
Sea : a=– 1 4 ,n=13,r=–2 1 4 + 1 4 =–2 u =a+( n–1 ) r u =– 1 4 +( 13–1 ) ( –2 ) u =– 1 4 +12( –2 ) u =– 1 4 –24 u =– 97 4 ↔ –24 1 4 - 19° término de
÷ –
5
6
.–
1
3
….
Sea : a=– 5 6 ,n=19,r=– 1 3 + 5 6 = 1 2 u =a+( n–1 ) r u =– 5 6 +( 19–1 ) ( 1 2 ) u =– 5 6 +18( 1 2 ) u =– 5 6 +9 u = 49 6 ↔ 8 1 6 - 33° término de
÷ 3
2
3
.2
11
12
….
Sea : a=3 2 3 ,n=33,r=2 11 12 –3 2 3 =– 3 4 u =a+( n–1 ) r u = 11 3 +( 33–1 ) ( – 3 4 ) u = 11 3 +32( – 3 4 ) u = 11 3 –24 u =– 61 3 ↔ –20 1 3 - 41° término de
÷ 2
4
5
.2
7
10
….
Sea : a=2 4 5 ,n=41,r=2 7 10 –2 4 5 =– 1 10 u =a+( n–1 ) r u =2 4 5 +( 41–1 ) ( – 1 10 ) u = 14 5 +40( – 1 10 ) u = 14 5 –4 u =– 6 5 ↔ –1 1 5 - 26° término de
÷ –
3
5
.
3
10
….
Sea : a=– 3 5 ,n=26,r= 3 10 + 3 5 = 9 10 u =a+( n–1 ) r u =– 3 5 +( 26–1 ) ( 9 10 ) u =– 3 5 +25( 9 10 ) u =– 3 5 + 45 2 u = 219 10 ↔ 21 9 10 - 19° término de
÷ –4.–
2
3
….
Sea : a=–4,n=19,r=– 2 3 +4= 10 3 u =a+( n–1 ) r u =–4+( 19–1 ) ( 10 3 ) u =–4+18( 10 3 ) u =–4+60 u =56 - 39° término de
÷ 3.–1
1
4
….
Sea : a=3,n=39,r=–1 1 4 –3=– 17 4 u =a+( n–1 ) r u =3+( 39–1 ) ( – 17 4 ) u =3+38( – 17 4 ) u =3– 323 2 u =– 317 3 ↔ –158 1 2