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

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

$1250= 10r^3$

$125= r^3$

$r=5$

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

$a_1=10/5$

$a_1= 2$

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

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

$log_5(15625)+1=n$

$6+1=7$

$n=7$