Identify type of series: Identify the type of series. The series 2017, 2018, ..., 2024 is an arithmetic series because the difference between consecutive terms is constant.Find first and last term: Find the first term (a_1) and the last term (a_n) of the series. The first term a_1 is 2017 and the last term a_n is 2024.Calculate number of terms: Calculate the number of terms (n) in the series. Since the series is consecutive integers from 2017 to 2024, we can find the number of terms by subtracting the first year from the last year and adding 1. n = 2024 - 2017 + 1 n = 7 + 1 n = 8Use formula for sum: Use the formula for the sum of an arithmetic series. The sum S_n of the first n terms of an arithmetic series is given by: S_n = n/2 * (a_1 + a_n)Substitute values into formula: Substitute the values into the formula to find the sum. S_8 = 8/2 * (2017 + 2024) S_8 = 4 * (4041) S_8 = 16164Verify the result: Verify the result. To check for a math error, we can quickly verify by adding the first and last term to see if it matches the sum we used in the formula: 2017 + 2024 = 4041 Since this matches the sum we used in the formula, it seems we have not made a math error.

Resources

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$2017+\ldots+2024$

View step-by-step help

Home

Math Problems

Algebra 2

Find the sum of a finite geometric series

Full solution

2017+\ldots+2024

Identify type of series: Identify the type of series. $\newline$ The series $2017$ , $2018$ , ..., $2024$ is an arithmetic series because the difference between consecutive terms is constant.
Find first and last term: Find the first term $a_1$ and the last term $a_n$ of the series. $\newline$ The first term $a_1$ is $2017$ and the last term $a_n$ is $2024$ .
Calculate number of terms: Calculate the number of terms $n$ in the series. $\newline$ Since the series is consecutive integers from $2017$ to $2024$ , we can find the number of terms by subtracting the first year from the last year and adding $1$ . $\newline$ $n = 2024 - 2017 + 1$ $\newline$ $n = 7 + 1$ $\newline$ $n = 8$
Use formula for sum: Use the formula for the sum of an arithmetic series. $\newline$ The sum $S_n$ of the first $n$ terms of an arithmetic series is given by: $\newline$ $S_n = \frac{n}{2} * (a_1 + a_n)$
Substitute values into formula: Substitute the values into the formula to find the sum. $\newline$ $S_8 = \frac{8}{2} \times (2017 + 2024)$ $\newline$ $S_8 = 4 \times (4041)$ $\newline$ $S_8 = 16164$
Verify the result: Verify the result. $\newline$ To check for a math error, we can quickly verify by adding the first and last term to see if it matches the sum we used in the formula: $\newline$ $2017 + 2024 = 4041$ $\newline$ Since this matches the sum we used in the formula, it seems we have not made a math error.