Find the 5^("th ") term of the arithmetic sequence -3x+3,4x-1,11 x-5,dots Answer:

Determine common difference: To find the 5th term of an arithmetic sequence, we need to determine the common difference between the 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, n is the term number, and d is the common difference.Find common difference: First, let's find the common difference (d) by subtracting the first term from the second term: (4x - 1) - (-3x + 3) = 4x - 1 + 3x - 3 = 7x - 4.Verify common difference: Now, let's verify the common difference by subtracting the second term from the third term: (11x - 5) - (4x - 1) = 11x - 5 - 4x + 1 = 7x - 4. Since the common difference is the same, we can confirm that the sequence is arithmetic.Calculate 5th term: Using the formula for the nth term of an arithmetic sequence, we can find the 5th term (a_5) as follows: a_5 = a_1 + (5 - 1)d = -3x + 3 + 4(7x - 4).Simplify expression: Now, let's simplify the expression for the 5th term: a_5 = -3x + 3 + 28x - 16 = 25x - 13.

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Find the
5^("th ") term of the arithmetic sequence
-3x+3,4x-1,11 x-5,dots
Answer:

Find the $5^{\text {th }}$ term of the arithmetic sequence $-3 x+3,4 x-1,11 x-5, \ldots$ $\newline$ Answer:

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Q. Find the

5^{\text {th }}

term of the arithmetic sequence

-3 x+3,4 x-1,11 x-5, \ldots

\newline

Answer:

Determine common difference: To find the $5^{\text{th}}$ term of an arithmetic sequence, we need to determine the common difference between the 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, $n$ is the term number, and $d$ is the common difference.
Find common difference: First, let's find the common difference $d$ by subtracting the first term from the second term: $(4x - 1) - (-3x + 3) = 4x - 1 + 3x - 3 = 7x - 4$ .
Verify common difference: Now, let's verify the common difference by subtracting the second term from the third term: $(11x - 5) - (4x - 1) = 11x - 5 - 4x + 1 = 7x - 4$ . Since the common difference is the same, we can confirm that the sequence is arithmetic.
Calculate $5$ th term: Using the formula for the nth term of an arithmetic sequence, we can find the $5$ th term $a_5$ as follows: $a_5 = a_1 + (5 - 1)d = -3x + 3 + 4(7x - 4)$ .
Simplify expression: Now, let's simplify the expression for the $5^{\text{th}}$ term: $a_5 = -3x + 3 + 28x - 16 = 25x - 13$ .