How do you write a rule for the nth term of the arithmetic sequence given #a_8=-44, a_5=-32#?

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Answer 1 · 2018-03-17T09:36:25

Therefore #color(brown)(a_n = -12 - 4n = -4(3 + n)#

#a_8 - a_5 = -44 - + 32 = -12#

But #a_8 - a_5 = 3 * d# where d is the common difference between successive terms.

#:. 3 d = -12# or #d = -4#

#a_2 = a_1 + d#

#a_3 = a_2 + d = a_1 + 2 d = a_1 + (3-1)#

Likewise, #a_5 = a_4 + d = a_1 + (5-1) * d = a_1 + (4 * -4) = a_1 - 16#

Hence, #a_1 = a_5 + 16 = -32 + 16 = -16#

#a_1 = -16, d = -4#

Therefore #a_n = a_1 + (n-1) * d = -16 + (n-1) * (-4)#

#=> -16 -4n + 4 = -12 - 4n#