Arithmetic Series

Question

The first term of an arithmetic series is 12 and the 5th term is -90. The series has 10 terms in total. What is the sum of this series?

Answer 1

x(n)=a+d(n-1) is the formula for a term

-90=12+d(5-1) because -90 is the 5th term

-90-12=d(4)

-102=4d

d=-102/4

d=-25.5  (common difference)

 

S(n)=(n/2)(2a+[n-1]d) is the formula for the sum

S(10)=(10/2)([2*12]+[10-1](-25.5))

S(10)=5(24+9[-25.5])

S(10)=5(24+[-229.5])

S(10)=5(-205.5)

S(10)=-1027.5  answer