Find the 14 th term of the arithmetic sequence x+8,8x+2,15 x-4,dots Answer:

Arithmetic Sequence Formula: To find the 14th term of an arithmetic sequence, we need to determine the common difference between consecutive terms and then use the formula for the nth term of an arithmetic sequence, which is a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference.Find Common Difference: First, let's find the common difference by subtracting the first term from the second term: (8x + 2) - (x + 8) = 7x - 6.Verify Common Difference: Now, let's verify the common difference by subtracting the second term from the third term: (15x - 4) - (8x + 2) = 7x - 6. Since the common difference is the same, we can confirm that the sequence is arithmetic.Calculate 14th Term: Using the common difference and the first term of the sequence, we can find the 14th term using the formula: a_14 = (x + 8) + (14 - 1)(7x - 6).Now, let's calculate the 14th term: a_14 = (x + 8) + 13(7x - 6) = (x + 8) + (91x - 78) = 92x - 70.

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Find the 14 th term of the arithmetic sequence
x+8,8x+2,15 x-4,dots
Answer:

Find the $14$ th term of the arithmetic sequence $x+8,8 x+2,15 x-4, \ldots$ $\newline$ Answer:

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Q. Find the

14

th term of the arithmetic sequence

x+8,8 x+2,15 x-4, \ldots

\newline

Answer:

Arithmetic Sequence Formula: To find the $14^{\text{th}}$ term of an arithmetic sequence, we need to determine the common difference between consecutive terms and then use the formula for the $n^{\text{th}}$ term of an arithmetic sequence, which is $a_n = a_1 + (n - 1)d$ , where $a_n$ is the $n^{\text{th}}$ term, $a_1$ is the first term, and $d$ is the common difference.
Find Common Difference: First, let's find the common difference by subtracting the first term from the second term: $(8x + 2) - (x + 8) = 7x - 6$ .
Verify Common Difference: Now, let's verify the common difference by subtracting the second term from the third term: $(15x - 4) - (8x + 2) = 7x - 6$ . Since the common difference is the same, we can confirm that the sequence is arithmetic.
Calculate $14$ th Term: Using the common difference and the first term of the sequence, we can find the $14$ th term using the formula: $a_{14} = (x + 8) + (14 - 1)(7x - 6)$ .
Calculate $14$ th Term: Using the common difference and the first term of the sequence, we can find the $14$ th term using the formula: $a_{14} = (x + 8) + (14 - 1)(7x - 6)$ .Now, let's calculate the $14$ th term: $a_{14} = (x + 8) + 13(7x - 6) = (x + 8) + (91x - 78) = 92x - 70$ .