How do you write a rule for the nth term of the arithmetic sequence and then find #a_10# for #1/4, 0, -1/4, -1/2, -3/4#?

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Answer 1 · 2018-02-03T06:49:59

#a_(10) = 2#

Given the Arithmetic sequence
# a_1 = (1/4), a_2 = 0, a_3 = -1/4, ...#

common difference #d = a_2 - a_1 = a_3 - a_2 = a4 -a_3# for A. P.

#d = 0 - 1/4 = -1/4#

#n^(th)# Term #a_n = a + ((n-1) * d) #

#10^(th) Term# #a_(10) = a +( (10-1) * d)#

#=> (1/4) + ( 10-1) * (-1/4)) = 1/4 - (9 * (1/4)) #

#=> 1/4 - 9/4 = 8/4 = 2#