Question

calculate S_24 for the arithmetic sequence in which a_13=1.9 and the common difference is d=3.7
a.-42.5
b.42.6
c.-59.4
d.1.2

Answer 1

an=a1+d(n-1)
a13=1.9
1.9=a1+3.7(13-1)
1.9=a1+3.7(12)
1.9=a1+44.4
minus 44.4 both sides
-42.5=a1

an=-42.5+3.7(n-1)
S_24, so sum all theway up to a24
S_n=(n(a1+an))/2

a1=-42.5
a24=-42.5+3.7(24-1)=42.6

S_n=(24(-42.5+42.6))/2
S_n=(24(0.1))/2
S_n=(2.4)/2
S_n=1.2

D