The second and fifth terms of a geometric sequence are 10 and 1250, respectively. Is 31,250 a term of this sequence? If so, which term is it?

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Answer 1 · 2018-07-19T03:30:07

Yes, it's the seventh term

#a_5= a_2(r)^(5-2)#

#1250= 10r^3#

#125= r^3#

#r=5#

#a_1= a_2(r)^(1-2)#

#a_1=10/5#

#a_1= 2#

#31,250= 2(5)^(n-1)#

#15625=(5)^(n-1)#

#log_5(15625)+1=n#

#6+1=7#

#n=7#