Question

A) In an arithmetic progression the sum of the first ten terms is 50 and the fifth term is three times the second term

(1) Calculate the first term
(2)Calculate the sum of the 20 terms

Answer 1

Just translate into Math using the definitions of AP

"the fifth term is three times the second term " ---> a+4d = 3(a+d)
a+4d = 3a+3d
d = 2a **

"the sum of the first ten terms is 50"
--> 5(2a+9d) = 50
2a+9d=10 ***

sub ** into ***
2a+9(2a) = 10
20a=10
a = 1/2
d = 1

first term is 1/2
sum(20)
= 10(2(1/2) + 19(1)) = 200

Answer 2

Just