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

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)