等差数列{an}中,an=29,Sn=155,d=3,求n和a1

Question

等差数列{an}中,an=29,Sn=155,d=3,求n和a1

Answer 1

a(n) = a + 3(n-1),
S(n) = na + 3n(n-1)/2,n = 1,2,...
29 = a + 3(n-1) = a + 3n - 3,
a = 32 - 3n
155 = na + 3n(n-1)/2 = n(32-3n) + 3n(n-1)/2
= 32n - 3n^2 + 3n^2/2 - 3n/2
= 61n/2 - 3n^2/2,
0 = 3n^2 - 61n + 310 = (3n - 31)(n - 10),
n = 10.
a = 32 - 3n = 32 - 30 = 2.