Final answer:
The nth term of the sequence 11, 61, 111, 161, 211 is given by nth term = 11 + 50(n - 1).
Step-by-step explanation:
To determine the nth term of the sequence 11, 61, 111, 161, 211, we can observe that the terms are increasing by 50 each time. So, the common difference is 50. Since the first term is 11, we can write the nth term as:
nth term = 11 + 50(n - 1)
This formula represents the pattern where n is the position of the term in the sequence. By substituting different values of n, we can find any term in the sequence
.To find the nth term of a given sequence, we can first determine if the sequence follows a specific pattern. In your provided sequence, which is: 11, 61, 111, 161, 211, ... we can observe that each term increases by the same amount. So, let's investigate the differences between the terms.
Between the first term (11) and the second term (61), the difference is: 61 - 11 = 50. Between the second term (61) and the third term (111), the difference is: 111 - 61 = 50. And this pattern continues with each subsequent term increasing by 50.
Since each term is increasing by a constant difference, we can conclude that this is an arithmetic sequence. The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n - 1) * d where: - a_n is the nth term we want to find, - a_1 is the first term of the sequence, - d is the common difference between the terms, - n is the term number. In this sequence: - a_1 (the first term) = 11, - d (the common difference) = 50. Plugging the values into the formula provides us with: a_n = 11 + (n - 1) * 50 Now we have a general formula for any term in the sequence.
To find a specific nth term, simply substitute the desired value of n into the formula and perform the arithmetic operation. For example, if you want to find the 10th term in the sequence, you would substitute 10 in for n: a_10 = 11 + (10 - 1) * 50 a_10 = 11 + 9 * 50 a_10 = 11 + 450 a_10 = 461 So, the 10th term in the sequence is 461. This process can be used for any value of n to determine any term in the sequence.