Find the 15^("th ") term of the arithmetic sequence 2x+5,8x+1,14 x-3,dots Answer:

Find Common Difference: To find the 15th term of the arithmetic sequence, we first need to determine the common difference (d) of the sequence. We can do this by subtracting the first term from the second term. Common difference (d) = (Second term) - (First term) d = (8x + 1) - (2x + 5)Calculate Common Difference: Now, let's perform the subtraction to find the common difference. d = 8x + 1 - 2x - 5 d = 6x - 4 The common difference of the sequence is 6x - 4.Use nth Term Formula: Next, we use the formula for the nth term of an arithmetic sequence, which is: nth term = a1 + (n - 1)d where a1 is the first term and n is the term number we want to find. In this case, a1 = 2x + 5 and n = 15. 15th term = (2x + 5) + (15 - 1)(6x - 4)Calculate 15th Term: Now we will calculate the 15th term by plugging in the values. 15th term = (2x + 5) + (14)(6x - 4) 15th term = (2x + 5) + (84x - 56)Combine Like Terms: Finally, we combine like terms to find the 15th term. 15th term = 2x + 5 + 84x - 56 15th term = 86x - 51

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Find the
15^("th ") term of the arithmetic sequence
2x+5,8x+1,14 x-3,dots
Answer:

Find the $15^{\text {th }}$ term of the arithmetic sequence $2 x+5,8 x+1,14 x-3, \ldots$ $\newline$ Answer:

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Math Problems

Grade 7

Evaluate variable expressions for Sequences

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Q. Find the

15^{\text {th }}

term of the arithmetic sequence

2 x+5,8 x+1,14 x-3, \ldots

\newline

Answer:

Find Common Difference: To find the $15^{\text{th}}$ term of the arithmetic sequence, we first need to determine the common difference ( $d$ ) of the sequence. We can do this by subtracting the first term from the second term. $\newline$ Common difference ( $d$ ) = (Second term) - (First term) $\newline$ $d = (8x + 1) - (2x + 5)$
Calculate Common Difference: Now, let's perform the subtraction to find the common difference. $\newline$ $d = 8x + 1 - 2x - 5$ $\newline$ $d = 6x - 4$ $\newline$ The common difference of the sequence is $6x - 4$ .
Use nth Term Formula: Next, we use the formula for the nth term of an arithmetic sequence, which is: $\newline$ nth term = $a_1 + (n - 1)d$ $\newline$ where $a_1$ is the first term and $n$ is the term number we want to find. In this case, $a_1 = 2x + 5$ and $n = 15$ . $\newline$ $15$ th term = $(2x + 5) + (15 - 1)(6x - 4)$
Calculate $15$ th Term: Now we will calculate the $15^{\text{th}}$ term by plugging in the values. $\newline$ $15^{\text{th}}$ term = $(2x + 5) + (14)(6x - 4)$ $\newline$ $15^{\text{th}}$ term = $(2x + 5) + (84x - 56)$
Combine Like Terms: Finally, we combine like terms to find the $15^{\text{th}}$ term.15^{\text{th}}\) term = 2x + 5 + 84x - 5615^{\text{th}}\) term = 86x - 51