How do you find the explicit formula for the following sequence 20,15,10,5,0?

1 Answer
Apr 12, 2016

Answer:

To find the explicit formula for an arithmetic sequence you must use the formula #t_n = a+ (n - 1)d#.

Explanation:

In the formula given above:

-#t_n# is the nth term

-#n# is the term's number in the sequence.

-#d# is the common difference separating the terms in your sequence

-#a# is the first term

#t_n = 20 + (n - 1)xx -5#

#t_n = 20 - 5n + 5#

#t_n = 25 - 5n#

This formula is now completely simplified, and as soon as you plug in a number for #n#, or a term, you can find it's term or it's number in the sequence, respectively.

Example

Find the 26th term in the sequence.

#t_26 = 25 - 5 xx 26#

#t_26 = 25 - 130#

#t_26 =-105#

Find which number of term has the value of #-60# in the sequence.

#-60 = 25 - 5n#

#-85 = -5n#

#17 = n#

Practice exercises:

  1. Consider the following sequence: #4, 11, 18, ...#

a) Find the explicit formula
b) Find the 37th term
c) Find the value of #n# if the term has a value of #74#

Good luck!