arithmetic sequence

Question

The model an = 395n + 5419 describes the cost of tuition and fees at public colleges in academic year n, where n = 1 corresponds to the school year ending in 2007, n = 2 to the school year ending in 2008, and so on.



Use this model and the formula for Sn to find the total cost of tuition and fees at public colleges for a four-year period from the school year ending in 2007 through the school year ending in 2010.

Answer 1

This is an arithmetic sequence that has 4 numbers in it, one for each of the 4 years.

 

One formula for the sum of a finite arithmetic sequence is S_n = n(a₁ + a_n) / 2

 

n is the number of terms, a₁ is the first term in the sequence, and a_n is the nth term.

 

So in this case...

 

n = 4

a₁ = 395(1) + 5419 = 5814

a_n = 395(4) + 5419 = 6999

 

So the sum of the four years would be 4 (5814 + 6999) / 2 = $25,626.