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

Answer 1

Lily Anderson

#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#

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Answer 2

Liam Brennan

#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#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.