Question

Write a rule for the n th term of the arithmetic sequence.

a_{12}=9,a_{27}=15

Answer 1

term(12) = 9 ----> a + 11d = 9
term(27) = 15 ---> a + 26d = 15
subtract them:
15d = 6
d = 6/15 = 2/5

sub into a + 11d = 9
a = 9 - 22/5 = 23/5

term(n) = a + (n-1)(d) = 23/5 + (n-1)(2/5)
= 23/5 + (2/5)n - 2/5
= (2/5)n + 21/5
= (2n + 21)/5

check:
term(12) = (24 + 21)/5 = 9
term(27) = (54 + 21)/5 = 15

my rule or formula for the nth term is correct