Write an expression to describe the sequence below. use n to represent the position of a term in the sequence, where n = 1 for the first term. -9, -18, -27, -36,

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

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