What is the general term of an arithmetic sequence with #t_1 = 5# and #t_2 = 2#?

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Answer 1 · 2017-04-13T16:08:44

#C#

The general term of an arithmetic sequence is given by

#t_n = a + (n - 1)d#.

We're given that the first term is #5# and the second term is #2#. This means that #d = -3#, so:

#a(n)= 5 - 3(n - 1)#

We note that #n < 1#, because if the sequence starts at #t_1#. Therefore, the domain is #n ≥ 1#.

If we check, we realize that

#a(1) = 5- 3(1- 1) = 5 = t_1#

Which is what we wanted to obtain.

Therefore, answer C is correct.

Hopefully this helps!