Answer:
[tex] \displaystyle \:a_n=- 6n + 31[/tex]
[tex] \displaystyle \:a_{52}= - 281[/tex]
Step-by-step explanation:
we are given some numbers
25,19,13,9
and said to figure out the sequence and 52 term
recall arithmetic sequence
[tex] \displaystyle \: a + (n - 1)d[/tex]
where a is the first term and d is the common difference
let's figure out d
[tex] \displaystyle \:d = 19 - 25 \\ d= - 6[/tex]
and a is 25
now we need to substitute the value of a and d and simplify to get our formula
substitute the value of a and d:
[tex] \displaystyle \: 25 + (n - 1) (- 6)[/tex]
distribute -6:
[tex] \displaystyle \: 25 + ( - 6n + 6)[/tex]
remove parentheses:
[tex] \displaystyle \: 25 - 6n + 6[/tex]
simplify addition:
[tex] \displaystyle \: - 6n + 31[/tex]
so our formula is -6n+31
remember here n means nth number term
we are said to figure out 52 number term
so
substitute the value of n:
[tex] \displaystyle \: - 6.52 + 31[/tex]
simplify multiplication:
[tex] \displaystyle \: - 312 + 31[/tex]
simplify addition:
[tex] \displaystyle \: - 281[/tex]
