Look at the pattern that follows. Which expression represents this pattern algebraically?
8, 17, 26, 35, 44, …
Common difference:
17 - 8 = 9
26 - 17 = 9
35 - 26 = 9
44 - 35 = 9
an = 8 + 9 * ( n - 1 ) = 8 + 9 n - 9 =
9 n - 1
n = 1
a1 = 9 * 1 - 1 = 9 - 1 = 8
n = 2
a2 = 9 * 2 - 1 = 18 - 1 = 17
n = 3
a3 = 9 * 3 - 1 = 27 - 1 = 26
n = 4
a4 = 9 * 4 - 1 = 36 - 1 = 35
n = 5
a5 = 9 * 5 - 1 = 45 - 1 = 44
To determine the algebraic expression that represents the given pattern, we need to identify the relationship between each term. By examining the pattern, we can see that each term is obtained by adding 9 to the previous term.
So, to express this pattern algebraically, we can use the expression:
8 + (n - 1) * 9
Where n represents the position of the term in the sequence.
To determine the algebraic expression that represents the given pattern, we need to identify the relationship between the terms. Looking at the pattern, we can observe that each term is obtained by adding 9 to the previous term.
To express this relationship algebraically, we start by defining the first term as an initial value, typically denoted as 'a'. In this case, the first term is 8.
Next, we represent the number of terms in the sequence with 'n'. Since the pattern does not specify a particular term number, we can generalize the relationship using 'n' as the position of any term.
Finally, we identify the common difference between the terms, which is the value added to each term to obtain the next term. In this case, the common difference is 9.
By applying these steps, we can determine the algebraic expression for this pattern:
Term = a + (n - 1) * d
Plugging in the values, we get:
Term = 8 + (n - 1) * 9
So, the algebraic expression that represents this pattern is:
Term = 8 + 9n - 9
Simplifying further, we get:
Term = 9n - 1