For a geometric sequence, t8 = 60 and t6 = 72, how do you find t10?

1 Answer
ProfLayton
Apr 22, 2016

#T_10=50#

Explanation:

The general formula for the #nth# term in a geometric sequence is this: #T_n=ar^(n-1)#
#T_8=ar^7=60#
#T_6=ar^5=72#, and know we have to solve for #r#, and we can do this by using the two information we have:
#T_8/T_6=60/72=(ar^7)/(ar^5)=r^2#
#60/72=r^2#
#5/6=r^2#
As you'll see, we don't need to square root #r^2#:
#T_10=ar^9#
#=ar^7*r^2#
#=T_8*r^2#
#=60*5/6#
#=50#

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