Question

sa se afle progresia aritmetica daca a1=33 si S26=1053***

Answer 1

Sn = (a1+an)*n/2 = a1*n + r*n(n-1)/2
S26 = (a1+a26)*26/12 = (33+a26) * 13 = 1053
33+a26 = 1053:13
a26 = 81-33
a26 = 48
Dar an = a1 + (n-1)*r
a26 = a1 + 25*r
48 = 33 + 25*r
25*r = 48-33 = 15
r = 15/25 = 3/5
r = 3/5

sau 

S26 = 33*26 + r*26*25/2 = 1053
858 + r*13*25 = 1053
325*r = 1053-858
325*r = 195
r = 195/325 = 39/65 = 3/5
r = 3/5