In a sequence of positive integers each term after the first is 1/3 of the sum of the term that precedes it and the term that follows it in the sequence. What is the 5th term of this sequence if the 1st term is 2 and the 4th term is 34?

Guest Nov 5, 2019

#1**+2 **

_{ the first is 1/3 of the sum of the term that precedes it and the term that follows it in the sequence}

2, x, y, 34

That is the sequence we have so far

Lets model an equation after that:

\(\frac{1}{3}(2+y)=x\)

\(\frac{1}{3}(x+34)=y\)

solve(1/3(2+y)=x, (1\3)(x+34)=y = {y=13, x=5}

Solving, we get the 3rd term being equal to 13.

Knowing that the third term is 13, the fourth term is 34, we can calculate the 5th term as follows:

\(\frac{1}{3}(13+x)=34\)

With x being the 5th term

(13+x)/3=34 = x=89

\(\boxed{89}\)

.CalculatorUser Nov 5, 2019