- #1
trulyfalse
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Hello everyone! My question is twofold. Firstly, how do I solve for term numbers in a geometric sequence and secondly, how do I algebraically solve for variables that are exponents?
Given the following geometric sequences, determine the number of terms, n.
t1=5
r (common ratio)=3
tn=135
tn=t1rn-1
where t1 is the first term
n is the number of terms
r is the common ratio
tn is the general term
I substituted in all known values yielding 135=(5)(3)n-1, which I simplified to 27=(3)n-1, leaving me stuck at the exponent variable. From here, how do I algebraically solve for the variable? Thanks!
Homework Statement
Given the following geometric sequences, determine the number of terms, n.
t1=5
r (common ratio)=3
tn=135
Homework Equations
tn=t1rn-1
where t1 is the first term
n is the number of terms
r is the common ratio
tn is the general term
The Attempt at a Solution
I substituted in all known values yielding 135=(5)(3)n-1, which I simplified to 27=(3)n-1, leaving me stuck at the exponent variable. From here, how do I algebraically solve for the variable? Thanks!