Given the Recursive Formula:
a1 = 5
a4 = an−1 +2
To find the next term in the sequence, we need to use the given recursive formula.
a1 = 5
a4 = an−1 +2
From the given information, we know that a4 is the 4th term in the sequence. This means that the value of n for a4 is 4. Substituting n = 4 into the recursive formula, we get:
a4 = a4−1 + 2
a4 = a3 + 2
To find a3, we can plug in n = 3 into the recursive formula:
a3 = a3−1 + 2
a3 = a2 + 2
Similarly, to find a2, we can plug in n = 2 into the formula:
a2 = a2−1 + 2
a2 = a1 + 2
Since the value of a1 is given as 5, we can substitute that into the equation to find a2:
a2 = 5 + 2
a2 = 7
Now that we know a2 is 7, we can substitute that into the equation to find a3:
a3 = 7 + 2
a3 = 9
Finally, we can substitute a3 into the equation to find a4:
a4 = 9 + 2
a4 = 11
Therefore, the next term in the sequence is 11.