Find the 14 th term of the arithmetic sequence x+3,7x-4,13 x-11,dots Answer:

Determine common difference: To find the 14th 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 find the common difference (d) by subtracting the first term from the second term: (7x - 4) - (x + 3) = 7x - 4 - x - 3 = 6x - 7.Calculate 14th term: Now that we have the common difference, we can use it to find the 14th term. The first term (a_1) is x + 3. Using the formula a_n = a_1 + (n - 1)d, we substitute n = 14, a_1 = x + 3, and d = 6x - 7.Substitute values: The calculation for the 14th term is as follows: a_14 = (x + 3) + (14 - 1)(6x - 7) = (x + 3) + 13(6x - 7).Simplify expression: Now, we simplify the expression: a_14 = x + 3 + 78x - 91 = 79x - 88.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the 14 th term of the arithmetic sequence
x+3,7x-4,13 x-11,dots
Answer:

Find the $14$ th term of the arithmetic sequence $x+3,7 x-4,13 x-11, \ldots$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Find trigonometric functions using a calculator

Full solution

Q. Find the

14

th term of the arithmetic sequence

x+3,7 x-4,13 x-11, \ldots

\newline

Answer:

Determine common difference: To find the $14^{th}$ 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 find the common difference $d$ by subtracting the first term from the second term: $(7x - 4) - (x + 3) = 7x - 4 - x - 3 = 6x - 7$ .
Calculate $14$ th term: Now that we have the common difference, we can use it to find the $14^{\text{th}}$ term. The first term ( $a_1$ ) is $x + 3$ . Using the formula $a_n = a_1 + (n - 1)d$ , we substitute $n = 14$ , $a_1 = x + 3$ , and $d = 6x - 7$ .
Substitute values: The calculation for the $14^{\text{th}}$ term is as follows: $a_{14} = (x + 3) + (14 - 1)(6x - 7) = (x + 3) + 13(6x - 7)$ .
Simplify expression: Now, we simplify the expression: $a_{14} = x + 3 + 78x - 91 = 79x - 88$ .