Find the 14 th term of the arithmetic sequence -2x+5,x+3,4x+1,dots Answer:

Find Common Difference: To find the 14th term of an arithmetic sequence, we need to determine the common difference between consecutive terms and then 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.Calculate Common Difference: First, let's find the common difference (d) by subtracting the first term from the second term. The second term is x+3 and the first term is -2x+5. d = (x + 3) - (-2x + 5)Use Formula for 14th Term: Simplify the expression to find the common difference. d = x + 3 + 2x - 5 d = 3x - 2Simplify Expression: Now, let's use the common difference to find the 14th term (a_14) using the formula a_n = a_1 + (n - 1)d. a_14 = (-2x + 5) + (14 - 1)(3x - 2)Find 14th Term: Simplify the expression to find the 14th term. a_14 = -2x + 5 + 13(3x - 2) a_14 = -2x + 5 + 39x - 26Combine Like Terms: Combine like terms to get the final expression for the 14th term. a_14 = 37x - 21

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
-2x+5,x+3,4x+1,dots
Answer:

Find the $14$ th term of the arithmetic sequence $-2 x+5, x+3,4 x+1, \ldots$ $\newline$ 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

-2 x+5, x+3,4 x+1, \ldots

\newline

Answer:

Find Common Difference: To find the $14^{th}$ term of an arithmetic sequence, we need to determine the common difference between consecutive terms and then 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.
Calculate Common Difference: First, let's find the common difference $d$ by subtracting the first term from the second term. The second term is $x+3$ and the first term is $-2x+5$ . $d = (x + 3) - (-2x + 5)$
Use Formula for $14^{\text{th}}$ Term: Simplify the expression to find the common difference. $\newline$ $d = x + 3 + 2x - 5$ $\newline$ $d = 3x - 2$
Simplify Expression: Now, let's use the common difference to find the $14$ th term $a_{14}$ using the formula $a_n = a_1 + (n - 1)d$ . $a_{14} = (-2x + 5) + (14 - 1)(3x - 2)$
Find $14^{\text{th}}$ Term: Simplify the expression to find the $14^{\text{th}}$ term. $a_{14} = -2x + 5 + 13(3x - 2)$ $a_{14} = -2x + 5 + 39x - 26$
Combine Like Terms: Combine like terms to get the final expression for the $14^{\text{th}}$ term. $a_{14} = 37x - 21$