176k views
1 vote
The sequence is 2, 14, 36, 68. Find the expression for the nth term of this sequence. Find the value of n and the corresponding value of the nth term.

1 Answer

4 votes

Final answer:

The sequence 2, 14, 36, 68 follows a quadratic pattern and its nth term is given by the formula T(n) = 2n² - n + 1. To find a specific term, such as the nth term, we substitute the value of n into the formula. For example, for n=5, the nth term would be 46.

Step-by-step explanation:

The sequence given is 2, 14, 36, 68, which seems to follow a quadratic pattern. To find the expression for the nth term of this sequence, we need to establish a rule that fits the given terms of the sequence. Observing the sequence, we can see that the differences between consecutive terms are increasing linearly: 12, 22, 32, ...—suggesting a quadratic pattern. Since the sequence does not start at 0, we should account for the constant term when deriving our nth term formula.

Let's attempt to derive the formula:
For n=1, we have 2; for n=2, we have 14, and so on.
So the nth term, T(n), could be represented in the form of an² + bn + c.
Using the sequence numbers for n=1, 2, 3, and 4, and solving the system of equations, we find that a=2, b=-1, and c=1.
Thus, the nth term of the sequence is T(n) = 2n² - n + 1.

To find a specific term in the sequence, such as the nth term, we simply substitute the value of n into the nth term formula. For example, for n=5, T(5) = 2(5)² - 5 + 1 = 2(25) - 5 + 1 = 50 - 5 + 1 = 46.

User Usman Iqbal
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories