What is the next term of the arithmetic sequence? -7,-12,-17", "

Identify sequence type: Identify the type of sequence. The sequence is given as -7, -12, -17. We need to determine if it is arithmetic or geometric. Since the difference between consecutive terms appears to be constant, we can say it is an arithmetic sequence.Find common difference: Find the common difference in the arithmetic sequence. To find the common difference, subtract the first term from the second term: -12 - (-7) = -12 + 7 = -5.Verify common difference: Verify the common difference with another pair of consecutive terms. Subtract the second term from the third term: -17 - (-12) = -17 + 12 = -5. The common difference is consistent, confirming that the sequence is arithmetic with a common difference of -5.Find next term: Find the next term in the sequence. Add the common difference to the last given term: -17 + (-5) = -17 - 5 = -22.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the next term of the arithmetic sequence?

-7,-12,-17", "

What is the next term of the arithmetic sequence? $\newline$ $-7,-12,-17 \text {, }$

View step-by-step help

Full solution

Q. What is the next term of the arithmetic sequence?

\newline

-7,-12,-17 \text {, }

Identify sequence type: Identify the type of sequence. $\newline$ The sequence is given as $-7, -12, -17$ . We need to determine if it is arithmetic or geometric. Since the difference between consecutive terms appears to be constant, we can say it is an arithmetic sequence.
Find common difference: Find the common difference in the arithmetic sequence. $\newline$ To find the common difference, subtract the first term from the second term: $-12 - (-7) = -12 + 7 = -5$ .
Verify common difference: Verify the common difference with another pair of consecutive terms. $\newline$ Subtract the second term from the third term: $-17 - (-12) = -17 + 12 = -5$ . The common difference is consistent, confirming that the sequence is arithmetic with a common difference of $-5$ .
Find next term: Find the next term in the sequence. $\newline$ Add the common difference to the last given term: $-17 + (-5) = -17 - 5 = -22$ .