How do I find the common ratio of an geometric sequence on a calculator?

Question

Benjamin Achtenberg · Accepted Answer

Assuming the terms are nonzero, we can find the common ratio #r# on a calculator by taking any two consecutive terms and dividing the later one by the earlier one:

#r= a_(n+1)/a_n# A geometric sequence is a sequence with a common ratio #r# between adjacent terms, that is, a sequence of the form #a_1, a_1r, a_1r^2, ..., a_1r^n, ...# Then, assuming the terms are nonzero, dividing any term by the prior term will give the common ratio: #(cancel(a_1)r^n)/(cancel(a_1)r^(n-1))=r^n/r^(n-1)=r^(n-(n-1))=r^1=r# To find #r# on a calculator, then, take any two consecutive terms and divide the later one by the earlier one. In fact, more generally, given any two terms #a_1r^m# and #a_1r^n#, #m < n#, we can find #r# by dividing #(a_1r^n)/(a_1r^m)# and taking the #(n-m)^"th"# root: #((a_1r^n)/(a_1r^m))^(1/(n-m)) = (r^(n-m))^(1/(n-m)) = r^((n-m)/(n-m))=r^1=r#

Ariana Alvarez · Answer

undefined To find the common ratio (r) of a geometric sequence on a calculator, you can use the formula:

r = (any term of the sequence) / (previous term)

1. Enter the value of any term in the geometric sequence.
2. Divide it by the value of the previous term in the sequence.
3. The result will be the common ratio (r) of the geometric sequence.