Sequence 80450

How many terms does the sequence have if a1=4, Sn=589, d=3, n=?

Correct answer:

n =  19

Step-by-step explanation:

a1=4 S=589 d=3  S = 2a1+an n S = 2a1+a1+(n1) d n  2 S=(a1+a1+(n1) d) n  2 589=(4+4+(n1) 3) n 3n25n+1178=0 3n2+5n1178=0  a=3;b=5;c=1178 D=b24ac=5243(1178)=14161 D>0  n1,2=2ab±D=65±14161 n1,2=65±119 n1,2=0.833333±19.833333 n1=19 n2=20.666666667  n=n1=19   Verifying Solution:   a19=a1+18 d=4+18 3=58  s19=2a1+a19 19=24+58 19=589

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