How do you write the nth term rule for the sequence #1, 3, 5, 7, 9, ...#?

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Answer 1 · 2016-09-11T13:02:33

#T_n = 2n -1#

This is clearly an arithmetic sequence because the terms differ by 2 each time.

To find the nth term rule we need:
a value for the first term , a
and a value for the common difference d .

These values are then plugged into the formula:

#T_n = a + (n-1)d#

#a = 1 and d = 2#

#T_n =a + (n-1)d#

#T_n = 1 + (n-1)2#

#T_n = 1 + 2n -2#

#T_n = 2n -1#

Answer 2 · 2016-09-11T13:22:58

#a_n = (2n-1) # for #n in NN#

This is the sequence of the odd positive integers where the #n^(th)# term #(a_n)# is:

#a_n = (2n-1) # for #n in NN#