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Instructions: For the following sequence, state the common difference, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.Sequence: 2,202,402,602,…2,202,402,602,…Common Difference: Answer 1 Question 10

Question

Instructions: For the following sequence, state the common difference, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.Sequence: 2,202,402,602,…2,202,402,602,…Common Difference: Answer 1 Question 10

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Solution

The common difference in the sequence 2, 202, 402, 602,... is 200. This is calculated by subtracting the first term from the second term (202 - 2 = 200), or the second term from the third term (402 - 202 = 200), and so on.

The explicit form of the rule for an arithmetic sequence is given by the formula a_n = a_1 + (n - 1) * d, where a_n is the nth term, a_1 is the first term, d is the common difference, and n is the position of the term in the sequence. For this sequence, the explicit form of the rule is a_n = 2 + (n - 1) * 200.

The recursive form of the rule for an arithmetic sequence is given by the formula a_n = a_(n-1) + d, where a_n is the nth term, a_(n-1) is the term before the nth term, and d is the common difference. For this sequence, the recursive form of the rule is a_n = a_(n-1) + 200.

To find the 10th term in the sequence, we can use the explicit form of the rule. Substituting n = 10 into the formula gives a_10 = 2 + (10 - 1) * 200 = 2 + 9 * 200 = 2 + 1800 = 1802. So, the 10th term in the sequence is 1802.

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