How do you write a rule for the nth term of the geometric sequence given the two terms #a_2=-153, a_4=-17#?

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Answer 1 · 2018-01-19T18:16:34

#u_n = +-459 * (+-1/3)^(n-1)#

geometric sequence: #u_n = ar^-1#

where #a# is the starting term

and #r# is the number by which one number is multiplied to make the next number in the sequence. (common ratio)

#u_2 = -153#
#u_4 = -17#

#u_2: n = 2#

#u_2 = ar^(2-1) = ar^1#

#u_2 = ar#

#u_4: n = 4#

#u_4 = ar^(4-1) = ar^3#

#ar = -153#
#ar^3 = -17#

#r^2 = (ar^3)/(ar) = (-17)/-153#

#r^2 = 1/9#

#r = +-1/3#

#ar = -153#

#r = +-1/3#

#a = -153 / ( +-1/3) = -153 * +-3#

#a = +-459#

the #n#th term of the geometric sequence is #u_n = +-459 * (+-1/3)^(n-1)#