How do you write a rule for the nth term of the arithmetic sequence given #a_9=-14, a_15=-20#?

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Answer 1 · 2018-02-08T11:22:45

#a_n = -(6 + (n-1))#

General equation of the #n^(th)# term of an arithmetic sequence is

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

#a_9 = a_1 + (9-1) d = -14# Eqn (1)

#a_(15) = a_1 + (15-1) d = -20# Eqn (2)

Subtraction Eqn(1) from (2),

#14d - 8d = -6#

#6d = -6# or #d = -1#

Substituting the value of d in Eqn (1),

#a_1 + (9* -1) = -14#

#a_1 = -14 +8 = -6#

#a_n = -6 +((n-1)*-1) = -(6 + (n-1))#