what are the three term of 2,8,26,80
what are the three terms of 36,69,135,267
huh? You just listed 4 terms, so which three do you want?
the first sequence is just 3^n - 1
the second can be written as
2^5 + 4, 2^6 + 5, 2^7 + 7, 2^8 + 9
So I think you made a typo, and the 1st term should be 35. In that case, then nth term is 16*2^n + 2n+1
To determine the three terms of the given sequence, we can look for a pattern:
Term 1: Start with 2
Term 2: Multiply the previous term by 4 = 8 (2 * 4 = 8)
Term 3: Multiply the previous term by 3 = 24 (8 * 3 = 24)
Term 4: Multiply the previous term by 4 = 96 (24 * 4 = 96)
Therefore, the three terms of the sequence are 2, 8, 24.
To find the pattern or relationship between the given terms, we can look for the ratio or the difference between consecutive terms. Let's calculate the ratios first:
8 / 2 = 4
26 / 8 = 3.25
80 / 26 ≈ 3.08
The ratios are not constant, so it seems that the relationship between the terms is not linear. Let's calculate the differences:
8 - 2 = 6
26 - 8 = 18
80 - 26 = 54
The differences are not constant either, so the pattern does not appear to be based on a simple arithmetic progression, where there is a constant difference between terms.
Let's look for a quadratic pattern by taking the ratios of the differences:
18 / 6 = 3
54 / 18 = 3
It appears that the ratios of the differences are constant, which suggests a quadratic relationship. We can try to find the quadratic equation that generates the terms.
Let the terms of the sequence be denoted by T(n), where n is the position of the term.
The quadratic equation can be expressed as:
T(n) = a * n^2 + b * n + c
Using the given terms, we can set up a system of equations and solve for the coefficients a, b, and c:
T(1) = a * 1^2 + b * 1 + c = 2
T(2) = a * 2^2 + b * 2 + c = 8
T(3) = a * 3^2 + b * 3 + c = 26
Solving this system of equations, we can find the values of a, b, and c. Once we have these coefficients, we can calculate upcoming terms by substituting different values of n into the quadratic equation.
Please note that without further context or additional terms, it is impossible to determine the exact pattern or predict future terms with absolute certainty.