Find the 1oth term of the arithmetic sequence -4x-5,x-8,6x-11,dots Answer:

Identify First Term: To find the 10th term of an arithmetic sequence, we need to determine the common difference and 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 identify the first term (a_1) of the sequence. The first term is given as -4x-5.Calculate 10th Term: Next, we need to find the common difference (d). We can do this by subtracting the first term from the second term. The second term is x-8. So, d = (x - 8) - (-4x - 5) = x - 8 + 4x + 5 = 5x + 3.Simplify Expression: Now that we have the common difference, we can use the formula to find the 10th term (a_10). a_10 = a_1 + (10 - 1)d = (-4x - 5) + 9(5x + 3).Let's simplify the expression for the 10th term. a_10 = -4x - 5 + 9(5x + 3) = -4x - 5 + 45x + 27 = 41x + 22.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the 1oth term of the arithmetic sequence
-4x-5,x-8,6x-11,dots
Answer:

Find the $1$ oth term of the arithmetic sequence $-4 x-5, x-8,6 x-11, \ldots$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Grade 7

Evaluate variable expressions for Sequences

Full solution

Q. Find the

1

oth term of the arithmetic sequence

-4 x-5, x-8,6 x-11, \ldots

\newline

Answer:

Identify First Term: To find the $10^{th}$ term of an arithmetic sequence, we need to determine the common difference and use the formula for the $n^{th}$ term of an arithmetic sequence, which is $a_n = a_1 + (n - 1)d$ , where $a_n$ is the $n^{th}$ term, $a_1$ is the first term, and $d$ is the common difference.
Find Common Difference: First, let's identify the first term $a_1$ of the sequence. The first term is given as $-4x-5$ .
Calculate $10$ th Term: Next, we need to find the common difference $d$ . We can do this by subtracting the first term from the second term. The second term is $x-8$ . $\newline$ So, $d = (x - 8) - (-4x - 5) = x - 8 + 4x + 5 = 5x + 3$ .
Simplify Expression: Now that we have the common difference, we can use the formula to find the $10^{\text{th}}$ term ( $a_{10}$ ). $\newline$ $a_{10} = a_1 + (10 - 1)d = (-4x - 5) + 9(5x + 3)$ .
Simplify Expression: Now that we have the common difference, we can use the formula to find the $10$ th term $a_{10}$ . $a_{10} = a_1 + (10 - 1)d = (-4x - 5) + 9(5x + 3)$ .Let's simplify the expression for the $10$ th term. $a_{10} = -4x - 5 + 9(5x + 3) = -4x - 5 + 45x + 27 = 41x + 22$ .