Answer:
The expression of this sequence is -9n
Step-by-step explanation:
* Lets revise the type of the sequence
- Arithmetic sequence:
- There is a constant difference between each two consecutive
numbers
* Ex:
# 2 , 5 , 8 , 11 , ……………………….
# 5 , 10 , 15 , 20 , …………………………
# 12 , 10 , 8 , 6 , ……………………………
* General term (nth term) of an Arithmetic Progression:
- U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d
- Un = a + (n – 1)d, where a is the first term , d is the difference
between each two consecutive terms
* Now lets look to the problem
- The sequence is : -9 , -18 , -27 , -36
∵ -18 - (-9) = -18 + 9 = -9
∵ -27 - (-18) = -27 + 18 = -9
∵ -36 - (-27) = -36 + 27 = -9
∴ The sequence is arithmetic with common difference -9
∵ a = -9 , d = -9 and n is the position of the term in the sequence
∴ The rule of the sequence is Un = -9 + (n -1)(-9)
* We can simplify it
∴ Un = -9 + n(-9) - (1)(-9) = -9 + (-9n) - (-9) = -9 - 9n + 9 = -9n
* The expression of this sequence is -9n
