Exercise 4 Page 439

Explicit equations for arithmetic sequences follow a specific format. a_n= a_1+( n-1) d In this form, a_1 is the first term in a given sequence, d is the common difference from one term to the next, and a_n is the nth term in the sequence. For this exercise, the first term is a_1= 13. To find the common difference d, we will subtract the first term from the second term. a_2-a_1=1/2-1/3=3/6-2/6=1/6 We can observe the other terms to confirm that this is actually the common difference. 1/3+ 16 ⟶1/2+ 16 ⟶2/3+ 16 ⟶5/6... By substituting d= 16 and a_1= 13 into the explicit equation and simplifying, we can find the formula for this sequence.

This equation can be used to find any term in the given sequence. To find a_(50), the 50th term in the sequence, we substitute 50 for n.

The 50th term in the sequence is 172. Note that we can also write it as a mixed number.