write a recursive formula for the sequence 15, 26, 48, 92, 180,... then find the next term
Looks to me like
an+1 = 2an - 4
To find a recursive formula for the given sequence, we need to look for a pattern. Let's examine the differences between consecutive terms:
26 - 15 = 11
48 - 26 = 22
92 - 48 = 44
180 - 92 = 88
We can observe that the differences between consecutive terms are themselves forming a pattern. The differences are doubling each time.
Let's denote the nth term of the sequence as a(n). The recursive formula for this sequence can be defined as:
a(n) = 2a(n-1) + 1
Using this formula, we can find the next term:
a(5) = 2a(4) + 1
= 2(180) + 1
= 361
Therefore, the next term in the sequence is 361.
To find a recursive formula for a sequence, we need to examine the pattern between consecutive terms. Looking at the given sequence: 15, 26, 48, 92, 180, ...
We can observe that each term is obtained by multiplying the previous term by 2 and then subtracting 2.
Let's define the recursive formula for this sequence:
a(1) = 15 (the first term)
a(n) = 2 * a(n-1) - 2 (for n > 1)
Using this formula, we can find the next term in the sequence:
a(1) = 15
a(2) = 2 * a(1) - 2 = 2 * 15 - 2 = 30 - 2 = 28
a(3) = 2 * a(2) - 2 = 2 * 28 - 2 = 56 - 2 = 54
a(4) = 2 * a(3) - 2 = 2 * 54 - 2 = 108 - 2 = 106
Therefore, the next term in the sequence is 106.