How do you write the expression for the nth term of the sequence given #3, 7, 11, 15, 19,...#?

1 Answer
Aug 31, 2017

#4n -1#

Explanation:

#3 , 7 , 11 , 15 ,19 ...#
is an arithmetic sequence. All arithmetic sequences can be written in the form #a + (n-1)d# where #a# is the first term in the sequence and #d# is the common difference . #n# represents the required term.

From example #a = 3 , d = 4# :

Hence #3 + (n - 1)4#

Expanding #3 + 4n - 4#

Collecting like terms #4n - 1#:

To check: The 4th term is #4# x #4 - 1 = 15#