The second and the 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?

1 Answer
Nov 15, 2015

Answer:

Yes it is a #7th# term; #a_7=31250#

Explanation:

To solve this task we have to find #a_1# and #q# first:

#a_2=10#

#a_5=1250#

#a_2*q^3=1250#

#10q^3=1250#

#q^3=125#

#q=5#

Now we can calculate #a_1=a_2/q=10/5=2#

Now we have to check if #31250# is a term of this sequence. To do this we have to solve equation:

#2*5^(n-1)=31250#

#5^(n-1)=15625#

#5^(n-1)=5^6#

#n-1=6#

#n=7#

The number would not be a term in this sequence if the solution of this equation was not a natural number.