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Given the sequence -7, 393, 793, 1193, 1593 Determine its nᵗʰ term

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Final answer:

The nᵗʰ term of the given sequence can be calculated using the formula n².

Step-by-step explanation:

The given sequence is: -7, 393, 793, 1193, 1593

By observing the pattern, we can see that the nth term can be calculated using the formula n2. So, to find the nth term, we need to substitute the value of n in the formula.

The student has provided a sequence: -7, 393, 793, 1193, 1593. To find the nᵗʰ term of this sequence, we can look for a pattern in the difference between consecutive terms. The differences are 400, 400, 400, and 400, indicating that we have an arithmetic sequence with a common difference (d) of 400.

To find the nᵗʰ term of an arithmetic sequence, we use the formula: Tn = a + (n - 1) * d, where Tn is the nᵗʰ term, a is the first term, and d is the common difference.

For this sequence, the first term (a) is -7 and the common difference (d) is 400. So, the formula becomes: Tn = -7 + (n - 1) * 400. Simplifying, we get: Tn = 400n - 407. This is the nᵗʰ term of the given sequence.

For example, if n = 1, the 1st term = 12 = 1. Similarly, for n = 2, the 2nd term = 22 = 4. And so on.

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