What is the general term of an arithmetic sequence with $t_{1} = 5$ $t_1 = 5$ and $t_{2} = 2$ $t_2 = 2$ ?

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Answer 1 · 2017-04-13T16:08:44

$C$ $C$

The general term of an arithmetic sequence is given by

$t_{n} = a + (n - 1) d$ $t_n = a + (n - 1)d$ .

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

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

We note that $n < 1$ $n < 1$ , because if the sequence starts at $t_{1}$ $t_1$ . Therefore, the domain is $n \geq 1$ $n ≥ 1$ .

If we check, we realize that

$a (1) = 5 - 3 (1 - 1) = 5 = t_{1}$ $a(1) = 5- 3(1- 1) = 5 = t_1$

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 t1=5t_1 = 5 and t2=2t_2 = 2?