How do you write the nth term rule for the arithmetic sequence with #d=-6# and #a_12=-4#?

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Answer 1 · 2016-11-05T01:40:01

#t_n = 68 - 6n#.

The nth term rule is given by #t_n = a + ( n- 1)d#, so we need to know the first term, #a#.

#t_n = a + (n - 1)d#

#-4 = a + (12 - 1)-6#

#-4 = a - 66#

#62 = a#

We can now reinsert inside the formula:

#t_n = a + (n - 1)d#

#t_n = 62 + (n - 1)-6#

#t_n = 62 - 6n + 6#

#t_n = 68 - 6n#

Hopefully this helps!