Answer:
subscripts identify different instances of objects that have a similar meaning or definition
Step-by-step explanation:
You apparently are interested in the meaning of the subscript N in the explicit formula ...
[tex]A_N=\dfrac{7N}{N+5}[/tex]
Here, it is used to identify different terms of a sequence. When a value is substituted for N, it replaces all instances of N. Using your example, the first three values of [tex]A_N[/tex] are ...
[tex]\text{for N=1: }A_1=\dfrac{7\cdot 1}{1+5}=\dfrac{7}{6}\\\\\text{for N=2: }A_2=\dfrac{7\cdot 2}{2+5}=\dfrac{14}{7}=2\\\\\text{for N=3: }A_3=\dfrac{7\cdot 3}{3+5}=\dfrac{21}{8}[/tex]
So, if you're asked to find the 20th term of the sequence, you put 20 where N is, then do the arithmetic.
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Subscripts are also used to identify elements of a matrix or coordinates in multiple dimensions. For this purpose, there may be 2 (or more) subscripts, whose order has meaning. The subscripts 24, for example, in [tex]A_{24}[/tex] refer to row 2, column 4 of a matrix named A. That is, the subscripts are in row, column order.
In short, subscripts are used to identify different instances of similar objects.
