Find the 1oth term of the arithmetic sequence -5x+5,x+1,7x-3,dots Answer:

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Find the 1oth term of the arithmetic sequence  -5x+5,x+1,7x-3,dots Answer:

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Find Common Difference: To find the 10th term of an arithmetic sequence, we first need to determine the common difference (d) between consecutive terms. Let's find the difference between the second and the first term. Subtract the first term from the second term: (x+1) - (-5x+5). Simplify the expression: x + 1 + 5x - 5. Combine like terms: 6x - 4.Calculate Differences: Now, let's find the difference between the third and the second term. Subtract the second term from the third term: (7x-3) - (x+1). Simplify the expression: 7x - 3 - x - 1. Combine like terms: 6x - 4.Confirm Arithmetic Sequence: We have found that the common difference (d) is 6x - 4 for both the first and second intervals. This confirms that the sequence is arithmetic and that the common difference is consistent.Use Formula for 10th Term: To find the 10th term (a_10), we use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1)d. Here, a_1 is the first term (-5x+5), n is the term number (10), and d is the common difference (6x - 4). Let's plug in the values: a_10 = (-5x+5) + (10 - 1)(6x - 4).Simplify 10th Term Calculation: Simplify the expression for the 10th term. First, calculate (10 - 1): 9. Then multiply 9 by the common difference (6x - 4): 9(6x - 4). This gives us: 54x - 36. Now add this to the first term (-5x+5): (-5x+5) + (54x - 36).Combine Terms for 10th Term: Combine like terms to find the 10th term. Add the x terms: -5x + 54x = 49x. Add the constant terms: 5 - 36 = -31. So, the 10th term is: 49x - 31.

Find the $1$ oth term of the arithmetic sequence $-5 x+5, x+1,7 x-3, \ldots$ $\newline$ Answer:

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