How do you write a rule for the nth term of the arithmetic sequence given #a_8=12#, #a_15=61#?

1 Answer
Aug 19, 2016

Answer:

The rule for this A.P. is # a_n = 7n-44#

Explanation:

To write a rue for an AP, we need to have the value for the first term,#a_1 and d#, the common difference.

Every term can be written in the general form of an AP,

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

In the terms we have been given we only know the values of #n# and #a_n#

Make 2 equations:

#" "a_8 = a_1 + 7d = 12" ...........................................A#
#" "a_15 = a_1 +14d = 61" .........................................B#

#B - A: " "7d = 49#
#" "d = 7#

Substitute 70 for d in A

# a_1 + 7(7) = 12 " "rArr a_1 = -37#

#a_n = -37 + (n-1)(7)#

#a_n = -37 +7n -7#

The rule for this A.P. is # a_n = 7n-44#