Use the formula for the nth term of an arithmetic sequence and the given terms to solve for d.
f(n)=6n + 17
Practice makes perfect
We can define an arithmetic sequence as a function of n.
f(n)=a_1+(n-1)d
This function generates the terms of any arithmetic sequence given a certain starting value a_1 and common difference d. The variable n is the independent variable and will always be a counting number. It represents the position of the term within the sequence. Therefore, the arithmetic sequence will have the following terms.
f(1), f(2), f(3), ...From the given diagram we can identify a few elements in our arithmetic sequence.
f(1)&=23 ⇒ a_1=23
f(4)&=41 ⇒ a_4=41
f(12)&=89 ⇒ a_(12)=89
We already know that the first term a_1 is 23.
f(n)= 23+(n-1)d
Now, to find the value of d, we will substitute the information for 4th term in the above equation. In other words, we will substitute 4 for n and 41 for f(n).
The common difference is 6. Let's use this information to write the function.
f(n)=23+(n-1) 6
Finally, let's distribute 6 in the above equation, and simplify the right-hand side.
