Find the 1 oth term of the arithmetic sequence -2x-3,4x+3,10 x+9,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, n is the term number, and d is the common difference.Find common difference: First, let's identify the first term (a_1) of the sequence. The first term given is -2x-3.Calculate 10th term: Next, we need to find the common difference (d). The common difference is the difference between any two consecutive terms. We can find it by subtracting the first term from the second term: (4x+3) - (-2x-3) = 4x + 3 + 2x + 3 = 6x + 6.Substitute values: Now that we have the first term and the common difference, we can find the 10th term (a_10) using the formula: a_10 = a_1 + (10 - 1)d.Simplify equation: Substitute the values into the formula: a_10 = (-2x-3) + (10 - 1)(6x + 6).Combine like terms: Simplify the equation: a_10 = -2x - 3 + 9(6x + 6) = -2x - 3 + 54x + 54.Final result: Combine like terms: a_10 = -2x + 54x - 3 + 54 = 52x + 51.The 10th term of the arithmetic sequence is 52x + 51.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the 1 oth term of the arithmetic sequence
-2x-3,4x+3,10 x+9,dots
Answer:

Find the $1$ oth term of the arithmetic sequence $-2 x-3,4 x+3,10 x+9, \ldots$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Solve exponential equations using natural logarithms

Full solution

Q. Find the

1

oth term of the arithmetic sequence

-2 x-3,4 x+3,10 x+9, \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, $n$ is the term number, and $d$ is the common difference.
Find common difference: First, let's identify the first term $a_1$ of the sequence. The first term given is $-2x-3$ .
Calculate $10$ th term: Next, we need to find the common difference $d$ . The common difference is the difference between any two consecutive terms. We can find it by subtracting the first term from the second term: $(4x+3) - (-2x-3) = 4x + 3 + 2x + 3 = 6x + 6$ .
Substitute values: Now that we have the first term and the common difference, we can find the $10$ th term ( $a_{10}$ ) using the formula: $a_{10} = a_1 + (10 - 1)d$ .
Simplify equation: Substitute the values into the formula: $a_{10} = (-2x-3) + (10 - 1)(6x + 6)$ .
Combine like terms: Simplify the equation: $a_{10} = -2x - 3 + 9(6x + 6) = -2x - 3 + 54x + 54$ .
Final result: Combine like terms: $a_{10} = -2x + 54x - 3 + 54 = 52x + 51$ .
Final result: Combine like terms: $a_{10} = -2x + 54x - 3 + 54 = 52x + 51$ .The $10$ th term of the arithmetic sequence is $52x + 51$ .