IDNLearn.com is your go-to resource for finding precise and accurate answers. Get accurate answers to your questions from our community of experts who are always ready to provide timely and relevant solutions.

What is the common difference between successive terms in the sequence?

[tex]\[9, 2.5, -4, -10.5, -17, \ldots\][/tex]


Sagot :

To determine the common difference in the given sequence [tex]\(9, 2.5, -4, -10.5, -17, \ldots\)[/tex], we need to find the differences between successive terms and observe if these differences are consistent.

Let's begin by calculating each difference step-by-step:

1. Calculate the difference between the second term ([tex]\(2.5\)[/tex]) and the first term ([tex]\(9\)[/tex]):
[tex]\[ 2.5 - 9 = -6.5 \][/tex]

2. Calculate the difference between the third term ([tex]\(-4\)[/tex]) and the second term ([tex]\(2.5\)[/tex]):
[tex]\[ -4 - 2.5 = -6.5 \][/tex]

3. Calculate the difference between the fourth term ([tex]\(-10.5\)[/tex]) and the third term ([tex]\(-4\)[/tex]):
[tex]\[ -10.5 - (-4) = -10.5 + 4 = -6.5 \][/tex]

4. Calculate the difference between the fifth term ([tex]\(-17\)[/tex]) and the fourth term ([tex]\(-10.5\)[/tex]):
[tex]\[ -17 - (-10.5) = -17 + 10.5 = -6.5 \][/tex]

After calculating these differences, we observe that each difference is [tex]\(-6.5\)[/tex]. Hence, the common difference between successive terms in the sequence is:
[tex]\[ \boxed{-6.5} \][/tex]