The largest and smallest of three consecutive terms in an arithmetic sequence differ by 14. Half of the smallest term is added to each term and the sum of the resulting three numbers is 120. What is the value of the original smallest term?

Guest Jun 26, 2018

#1**+2 **

Let the smallest term = a

Let the next term = a + d

Let the largest term be a + 2d

And we know that

(a + 2d) - a = 14

2d = 14

d = 7

So we have that

a + a/2 + (a + 7) + a/2 + (a + 14) + a/2 = 120 simplify

3a + 3a/2 + 21 = 120

4.5a + 21 = 120 subtract 21 from both sides

4.5 a = 99 divide both sides by 4.5

a = 22

So...the smallest term is 22

CPhill Jun 27, 2018