To find the missing number in the sequence –5, –15, –45, ____, –405, –1,215, let's first look at how the numbers change from one to the next.
We can observe the ratios between consecutive numbers:
-
From –5 to –15: \(-15 / -5 = 3\)
-
From –15 to –45: \(-45 / -15 = 3\)
It appears that each number is multiplied by 3 to get to the next.
Following this pattern:
To find the missing number, multiply –45 by 3:
\(-45 \times 3 = -135\)
Now, let's check if the pattern holds for the subsequent numbers:
-
From –135 to –405: \(-405 / -135 = 3\)
-
From –405 to –1,215: \(-1,215 / -405 = 3\)
All divisions confirm that the numbers are indeed multiplied by 3.
Thus, the missing number in the sequence is:
\(-135\)