How do you write a rule for the nth term of the arithmetic sequence #a_7=21, a_13=42#?

1 Answer
Apr 11, 2017

Answer:

#a_n = 7/2(n-1)#

Explanation:

Arithmetic sequence, #a_n = a_1 + (n-1)d#, d=common difference.

given that,
#a_7 = 21#
# a_1 + (7-1)d = 21#
# a_1 + 6d = 21 ->#A

#a_13 = 42#
#a_1 + 12d = 42->#B

B-A,
#6d =21# #->d =21/6 = 7/2#

Plug in #d = 7/2# in A or B.
# a_1 + 6(7/2) = 21 #
# a_1 + 21 = 21 # #->a_1 = 0#

therefore,
#a_n = 0 + (n-1)7/2#
#a_n = 7/2(n-1)#