Solution for Problem 8.3.1

  Find the nth term of the following sequence   29, 25, 21, 17, 13, ...
  Then find the 25th term.

Solve

Step

= 13 - 17 = -4,   = 17 - 21 = -4  
= 21 - 25 = -4,   = 25 - 29 = -4  

Find the common difference. 
d = -4

an = a1 + (n - 1)

Use the formula for arithmetic sequence since there is a common difference.

a1 = 29 and   d = -4

a1 = 29 is the first term of the sequence.

an = 29 + (n - 1)(-4

Plug in the values and simplify.

an = 29 - 4n + 4 = -4n + 33

an -4n + 33

nth term

a50 -4(50) + 33 = -200 + 33 = -167

50th term  

Spot Check

a1 -4(1) + 33 = -4 + 33 = 29

a3 -4(3) + 33 = -12 + 33 = 21

a5 = -4(5) + 33 = -20 + 33 = 13