The quantity of interest in a discrete
dynamical system is sequence of values denoted by {xk}, or completely written out
x0, x1, x2, . . . , xk, . . . , (2)
where x0 represents the value at the beginning of the initial time period, x1, the value at the end of the
first time period, and xk, the value at the end of the kth time period.
http://www4.ncsu.edu/~njrose/pdfFiles/Ma303.pdf

Note: 1, 2 ... k are subscripts, while 'th' is superscript (upper index, not to confuse with 'exponent').


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Note added at 3 hrs (2012-12-08 08:58:49 GMT)
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Other notations are alos common:

Outstanding pricipal at beginning of the kth period
http://www.math.utah.edu/~jp/M1090Spring07_files/Formulashee...

during each kth period (k is an integer from 0 to n) of successive periods from the zeroth period to a nth period (n is an integer) which is a horizontal period
http://www.google.com/patents/US20120127153

7. The first two terms in a sequence are x1 = 1 and x2 = 1. Thereafter, each term is the sum of the
preceding two terms. Write out the first 5 terms of the sequence and set up a difference equation, with
proper initial conditions, for the nth term.
http://www4.ncsu.edu/~njrose/pdfFiles/Ma303.pdf
(same article, same superscription)

kth term test
P1
k=1 ak diverges if
lim
k!1
ak 6= 0.
This test gives no information about the convergence of the series.
http://www4.ncsu.edu/~njrose/pdfFiles/Ma303.pdf