the following series is arithmetic: 5+8+11+...+116

Question

I have to show how I arrived at the following:

a) determine the number of terms in this series.

b) determine the sum of this series.

 

Answer 1

5+8+11+...+116

x(n)=a+d(n-1)   a=first term, d=common difference, n=term

116=5+3(n-1)

116=5+3n-3

116=2+3n

116-2=3n

114=3n

n=114/3

n=38 terms

 

S(n)=(n/2)(2a+[n-1]d)

S(38)=(38/2)(10+37*3)

S(38)=19(10+111)

S(38)=19(121)

S(38)=2299