To find the recursive formula for this sequence, we need to determine the pattern in which each term is related to the previous term(s).
Looking at the differences between consecutive terms, we can see that the differences are increasing by 11 each time: 26-15 = 11, 48-26 = 22, 92-48 = 44.
From this observation, we can say that the differences between consecutive terms form an arithmetic sequence with a common difference of 11.
To find the pattern in the terms themselves, we notice that each term is obtained by multiplying the previous term by 2 and then subtracting a certain value.
The first term can be expressed as 15 = 2^1 * 15 - 15.
The second term can be expressed as 26 = 2^2 * 15 - 4.
The third term can be expressed as 48 = 2^3 * 15 - 8.
The fourth term can be expressed as 92 = 2^4 * 15 - 12.
From this pattern, we can generalize that the nth term can be expressed as:
Term(n) = 2^(n-1) * 15 - (2^n - 1) * 4
Therefore, the recursive formula for this sequence is:
Term(n) = Term(n-1) + 11, with the initial term Term(1) = 15.
What is the recursive formula for the sequence?
15, 26, 48, 92, . . .
1 answer