Write a recursive formula for the sequence 15, 26, 48, 92, 180, ... Then find the next term.
x*2-4
180*2-4=356
2(x-2)
2(180-2)=360-4=356
To find the recursive formula for the given sequence, we need to look for a pattern in the differences between consecutive terms.
Looking at the differences:
26 - 15 = 11
48 - 26 = 22
92 - 48 = 44
180 - 92 = 88
From these differences, we can see a pattern emerge. Each difference is twice the previous difference.
Therefore, the recursive formula for the given sequence is:
a(n) = 2 * a(n-1) + 2
Using this formula, we can find the next term by substituting the value of n into the formula and solving for a(n). However, since we are not given a specific value of n, we cannot find the exact next term.
If we assume that the sequence continues with the pattern, we can plug in n = 5 since the pattern starts with the term 15. By substituting n = 5 into the formula, we can find the next term as follows:
a(5) = 2 * a(5-1) + 2
a(5) = 2 * a(4) + 2
a(5) = 2 * 180 + 2
a(5) = 360 + 2
a(5) = 362
Therefore, assuming the pattern continues, the next term in the sequence is 362.
To find a recursive formula for the given sequence, we'll need to identify the pattern or rule that generates each term based on the previous terms.
Let's take a closer look at the given sequence: 15, 26, 48, 92, 180, ...
To get from 15 to 26, we multiply 15 by 1 and add 11: 15 * 1 + 11 = 26.
To get from 26 to 48, we multiply 26 by 1 and add 22: 26 * 1 + 22 = 48.
To get from 48 to 92, we multiply 48 by 1 and add 44: 48 * 1 + 44 = 92.
To get from 92 to 180, we multiply 92 by 1 and add 88: 92 * 1 + 88 = 180.
From these observations, we can see that each term is obtained by multiplying the previous term by 1 and adding a specific number. Thus, we can write the recursive formula as:
a[n] = a[n-1] * 1 + k,
where a[n] represents the nth term of the sequence, a[n-1] is the previous term, and k is a constant number.
In this case, the constant number k increases with each term. Let's calculate the values of k for each term:
k = 11 (from 15 to 26)
k = 22 (from 26 to 48)
k = 44 (from 48 to 92)
k = 88 (from 92 to 180)
So, we can now rewrite our recursive formula as:
a[n] = a[n-1] * 1 + k[n-1],
where k[n-1] represents the value of k for the (n-1)th term.
Now, to find the next term in the sequence, we need to find the value of k[5] (for the 5th term):
k[5] = 2 * k[5-1] = 2 * 88 = 176.
Finally, we can calculate the next term:
a[6] = a[5] * 1 + k[5] = 180 * 1 + 176 = 356.
Therefore, the next term in the sequence is 356.