The eighth number of a list of two-digit code numbers is 24. If each number after the first number in the list is four less than the number immediately preceding it, what is the fourth code number in the list?

Question

campbell_st · Answer

this is an arithmetic sequence. 

there are several parts to the question 

1. you need to find the 1st number on the pattern 

2. then find the 4th number

you know the 8th number and you know the common difference  

so you can use the formula 

$$a_{n} = a_{1} + ( n - 1) \times d$$

so for the 8th number you know 

$$a_{8} = 24....n = 8....d = -4$$

substitute then to find the 1st number. 

when you have the 1st number, you can use the same formula to find the 4th number. 

n = 4, d = -4 and you have found the 1st number. 

hope this helps.