A sequence is generated in which each term is 9 more than the previous term, If the eighth term is 13, what is the fourth term?

a. -23
b. -14
c. 40
d. 49
e. 58

please answer and explain

Since T4 is 4 terms before T8,

13 - 4(9) = ?

To find the fourth term of the sequence, we need to find the common difference first.

Since each term is 9 more than the previous term, the common difference is 9.

Let's denote the first term of the sequence as 'a'.
Then, the second term would be a + 9, the third term would be a + 9 + 9, and so on.

So, the eighth term can be represented as a + (8 - 1) * 9 = a + 7 * 9 = a + 63.

Given that the eighth term is 13, we have the equation:
a + 63 = 13.

Simplifying the equation, we get:
a = 13 - 63 = -50.

Now, we can find the fourth term:
The fourth term is a + (4 - 1) * 9 = -50 + 3 * 9 = -50 + 27 = -23.

Therefore, the fourth term of the sequence is -23.
The correct option is (a) -23.