17. Sn = n² + an + b a1 = 2
Sn = (a1 + an)· n /2 Sn = [2 + 2 + (n-1)r]·n/2 = [4 +n·r - r]·n/2
Sn = 2n + n²/2 ·r - n·r/2
n² + a·n + b = n²·r/2 + (2 - r/2)·n
1 = r/2 r = 2 a = 1 b = 0
18. a + a+r + a + 2r = 12 3a + 3r = 12 a + r = 4
(a+1), (a+r +2), ( a + 2r + 11)
(a +1), 6 , (r + 15)
(a+1)·q = 6 a = (6-q)/q
6q = r + 15 r = 6q -15 4 = (6-q)/q + 6q - 15
4q = 6-q + 6q² - 15q
6q² - 20q + 6 = 0 3q² -10q + 3 = 0 3q (q - 3) - (q - 3) = 0 (q-3)(3q-1)= 0
q = 3 r = 3 a = 1
progresia aritmetica : 1,4,7, 10....
progresia geometrica : 2,6,11.....
q = 1/3 r = - 13 a = 17
progresia aritm. 17,4,-9,-22....
progresia geom. 18,6,2,.....
