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!

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