How do you find the next four terms of the arithmetic sequence 9, 16, 23, ...?

2 Answers
Jul 4, 2017

Answer:

See the explanation below.

Explanation:

In this arithmetic sequence, the common difference #d# is 7. You can find this by subtracting a term from the consecutive term: 16 - 9 = 7, 23 - 16 = 7.

In order to find the next four terms, keep adding 7 to the previous term.

23 + 7 = 30
30 + 7 = 37
37 + 7 = 44
44 + 7 = 51

The next four terms are 30, 37, 44, and 51.

Jul 4, 2017

From the reference Arithmetic Progression we obtain the following equation:

#a_n = a_1 + d(n-1)#

where #a_n# is the nth term, #a_1# is the first term, #d# is the difference between each term and #n# is any integer greater than 0.

From the sequence we observe that #a_1 = 9# and #d = 7#; this gives use the following equation:

#a_n = 9 + 7(n-1)#

This equation allows us to compute the next 4 terms:

#a_4 = 9 + 7(4-1) = 30#
#a_5 = 9 + 7(5-1) = 37#
#a_6 = 9 + 7(6-1) = 44#
#a_7 = 9 + 7(7-1) = 51#