First term in arithmetic series is 3, last is 136, sum is 1,390, what are first 3 terms?

Question

College algebra placement testing.  Want to know how to work this out.

Answer 1

In arthimetic series a n = a+(n-1)d

s n = n/2(a+l)

Here a = 3,  l = 136

a = first term , d = common difference.

l =last term.

1390 = n/2(3+136)

2*1390 = n(139)

2780 = 139n

n = 2780/139

n = 20

a n = 3+(20-1)d

136 = 3+19d

136-3 = 19d

133 = 19d

133/19 = d

d = 7

First term = a = 3

Second term = a+d = 3+7 = 10

Third term = a+2d = 3+2*7 = 17.

Comments

good answer