Question

ma ajutati la 17 si 18 mersi :)

Answer 1

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,.....