Question

26. The first term in an arithmetic sequence is -3. The sequence has a common difference of 8, what is the 30th term in the sequence? a.) Find the first five terms of the sequence. c b.) Write the rule for the sequence. an = a1 + (n − 1)d c.) Find the 30th term of the sequence?

Answer 1

Answer:

(a) The first five terms are:

-3, 5, 13, 21, 29

(b) The rule for the sequence is:

`T_n=-3+8(n-1)`

(c) The 30th term is 229

Step-by-step explanation:

Let the given first term be a = -3

The common difference be d = 8

The nth term of this sequance is:

`T_n=-3+(n-1)d`

The first five terms are:

a, a + d, a + 2d, a + 3d, and a + 4d

a = -3

a + d = -3 + 8 = 5

a + 2d = -3 + 2(8) = 13

a + 3d = -3 + 3(8) = 21

a + 4d = -3 + 4(8) = 29

Putting n = 30, the 30th term is:

`\begin{gathered} T_(30)=-3+(30-1)(8)_{} \\ =-3+29(8) \\ =-3+232 \\ =229 \end{gathered}`