To solve for the missing number and understand the pattern in the given sequence [tex]\(1, -3, -10, 24\)[/tex], we need to examine the differences between consecutive terms.
1. Calculate the first difference (difference between the first and second term):
[tex]\[
a = -3 - 1 = -4
\][/tex]
2. Calculate the second difference (difference between the second and third term):
[tex]\[
b = -10 - (-3) = -10 + 3 = -7
\][/tex]
3. Calculate the third difference (difference between the third and fourth term):
[tex]\[
c = 24 - (-10) = 24 + 10 = 34
\][/tex]
Thus, the pattern of the differences between the consecutive terms in the series [tex]\(1, -3, -10, 24\)[/tex] can be summarized as follows:
[tex]\[
a = -4, \quad b = -7, \quad c = 34
\][/tex]
