We want write the recursive rule and the explicit rule for the given sequence. Let's pay close attention to the difference between consecutive terms.
7 + 6 ⟶ 13 + 6 ⟶ 19+ 6 ⟶ 25 + 6 ⟶ 31 + 6 ⟶ ...
We can see that the difference between consecutive terms is 6. Therefore, the given sequence is an arithmetic sequence.
Recursive Rule
Let's now consider the general formula for a recursive rule.
a_1& =a
a_n&=a_(n-1)+d,forn≥ 2
In the above formula, a is the first term of the sequence and d is the common difference.
For our sequence, the first term is 7 and the common difference is 6.
a_1& = 7
a_n&=a_(n-1)+ 6,forn≥ 2
Explicit Rule
Finally, let's recall the general formula of the explicit rule for an arithmetic sequence.
a_n=a_1+d(n-1)
Here, a_1 represents the first term of the sequence and d is the common difference. As we have already stated, for our sequence, we have a= 7 and d= 6.
a_n= 7+ 6(n-1)
Finding the 12th Term
To find the value of the 12th term, we substitute n= 12 into this equation and evaluate the right-hand side.
