Find the 6 th term of the arithmetic sequence x+5,4x+7,7x+9,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. Common difference (d) = (4x + 7) - (x + 5) d = 4x + 7 - x - 5 d = 3x + 2Find nth term formula: Use the common difference to find the nth term formula. The nth term of an arithmetic sequence can be found using the formula: nth term = first term + (n - 1) * common difference We already have the first term (x + 5) and the common difference (3x + 2).Calculate 6th term: Calculate the 6th term using the nth term formula. 6th term = (x + 5) + (6 - 1) * (3x + 2) 6th term = (x + 5) + 5 * (3x + 2) 6th term = (x + 5) + (15x + 10) 6th term = x + 5 + 15x + 10 6th term = 16x + 15

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Find the 6 th term of the arithmetic sequence
x+5,4x+7,7x+9,dots
Answer:

Find the $6$ th term of the arithmetic sequence $x+5,4 x+7,7 x+9, \ldots$ $\newline$ Answer:

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Math Problems

Grade 8

Evaluate variable expressions for sequences

Full solution

Q. Find the

6

th term of the arithmetic sequence

x+5,4 x+7,7 x+9, \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. $\newline$ Common difference $d$ = $(4x + 7) - (x + 5)$ $\newline$ $d = 4x + 7 - x - 5$ $\newline$ $d = 3x + 2$
Find nth term formula: Use the common difference to find the nth term formula. $\newline$ The nth term of an arithmetic sequence can be found using the formula: $\newline$ nth term = first term + $(n - 1) \times \text{common difference}$ $\newline$ We already have the first term $(x + 5)$ and the common difference $(3x + 2)$ .
Calculate $6$ th term: Calculate the $6$ th term using the nth term formula. $\newline$ $6$ th term $= (x + 5) + (6 - 1) \times (3x + 2)$ $\newline$ $6$ th term $= (x + 5) + 5 \times (3x + 2)$ $\newline$ $6$ th term $= (x + 5) + (15x + 10)$ $\newline$ $6$ th term $= x + 5 + 15x + 10$ $\newline$ $6$ th term $= 16x + 15$