Find the 5^("th ") term of the arithmetic sequence 2x+2,5x+6,8x+10,dots Answer:

Identify common difference: Identify the common difference of the arithmetic sequence. To find the common difference, we subtract the first term from the second term. Calculation: (5x + 6) - (2x + 2) = 3x + 4Verify common difference: Verify the common difference by subtracting the second term from the third term. Calculation: (8x + 10) - (5x + 6) = 3x + 4 This confirms that the common difference is indeed 3x + 4.Find 5th term: Use the common difference to find the 5th term. The nth term of an arithmetic sequence can be found using the formula: nth term = first term + (n - 1) * common difference. For the 5th term, n = 5. Calculation: 5th term = (2x + 2) + (5 - 1) * (3x + 4)Simplify expression: Simplify the expression for the 5th term. Calculation: 5th term = (2x + 2) + 4 * (3x + 4) 5th term = (2x + 2) + (12x + 16) 5th term = 2x + 2 + 12x + 16 5th term = 14x + 18

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Grade 7

Add integers

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Q. Find the

5^{\text {th }}

term of the arithmetic sequence

2 x+2,5 x+6,8 x+10, \ldots

\newline

Answer:

Identify common difference: Identify the common difference of the arithmetic sequence. $\newline$ To find the common difference, we subtract the first term from the second term. $\newline$ Calculation: (\(5x + $6$ ) - ( $2$ x + $2$ ) = $3$ x + $4$
Verify common difference: Verify the common difference by subtracting the second term from the third term. $\newline$ Calculation: $(8x + 10) - (5x + 6) = 3x + 4$ $\newline$ This confirms that the common difference is indeed $3x + 4$ .
Find $5$ th term: Use the common difference to find the $5$ th term. The $n$ th term of an arithmetic sequence can be found using the formula: $n$ th term = first term + ( $n$ - $1$ ) * common difference. For the $5$ th term, $n = 5$ . Calculation: $5$ th term = ( $2x + 2$ ) + ( $5$ - $1$ ) * ( $3x + 4$ )
Simplify expression: Simplify the expression for the $5^{\text{th}}$ term. $\newline$ Calculation: $5^{\text{th}}$ term = $(2x + 2) + 4 \times (3x + 4)$ $\newline$ $5^{\text{th}}$ term = $(2x + 2) + (12x + 16)$ $\newline$ $5^{\text{th}}$ term = $2x + 2 + 12x + 16$ $\newline$ $5^{\text{th}}$ term = $14x + 18$