Sure, let's analyze the given sequence: \(-5, -2, 4, 13\).
First, we calculate the differences between consecutive terms:
[tex]\[
-2 - (-5) = 3
\][/tex]
[tex]\[
4 - (-2) = 6
\][/tex]
[tex]\[
13 - 4 = 9
\][/tex]
These differences form the sequence: \(3, 6, 9\).
Next, we observe the pattern in these differences. Here, each term is increasing by 3:
[tex]\[
6 - 3 = 3
\][/tex]
[tex]\[
9 - 6 = 3
\][/tex]
Given this consistent increase, the next difference after 9 would logically be:
[tex]\[
9 + 3 = 12
\][/tex]
To find the next term in the original sequence, we add this next difference to the last term of the sequence:
[tex]\[
13 + 12 = 25
\][/tex]
So, the next number in the sequence is indeed [tex]\(25\)[/tex]. Therefore, the conjecture is [tex]\( \boxed{\text{True}} \)[/tex].
