Question

type the missing number in this sequence:
□, -53, -60, -67, -74

Explanation:

Step1: Find the common difference

To find the common difference, we subtract consecutive terms. Let's take the second term and subtract the third term: $-53 - (-60) = -53 + 60 = 7$. Wait, actually, to find the common difference $d$ in an arithmetic sequence, we can do $a_{n + 1}-a_{n}$. Let's check between $-60$ and $-67$: $-67 - (-60)=-67 + 60=-7$. Similarly, $-74 - (-67)=-74 + 67=-7$. So the common difference $d=-7$.

Step2: Find the missing term

The missing term is before $-53$. In an arithmetic sequence, the term before a given term $a_{n}$ is $a_{n}-d$. Here, $a_{2}=-53$ and $d = - 7$, so the first term $a_{1}=a_{2}-d=-53-(-7)=-53 + 7=-46$.

Answer:

-46