Answer :
To determine the common difference between successive terms in the sequence [tex]\(0.36, 0.26, 0.16, 0.06, -0.04, -0.14, \ldots\)[/tex], we can follow these steps:
1. Select Consecutive Terms: Choose the first two terms of the sequence for calculation, which are [tex]\(0.36\)[/tex] and [tex]\(0.26\)[/tex].
2. Calculate the Difference: Subtract the second term from the first term. The formula for the common difference [tex]\(\delta\)[/tex] is given by:
[tex]\[ \delta = \text{Next term} - \text{Previous term} \][/tex]
Specifically, here:
[tex]\[ \delta = 0.26 - 0.36 \][/tex]
3. Perform the Subtraction: Compute the value:
[tex]\[ \delta = 0.26 - 0.36 = -0.10 \][/tex]
4. Verify the Consistency: Optionally, you can check whether the difference is consistent between other successive terms to confirm it. For example:
[tex]\[ 0.16 - 0.26 = -0.10 \][/tex]
[tex]\[ 0.06 - 0.16 = -0.10 \][/tex]
[tex]\[ -0.04 - 0.06 = -0.10 \][/tex]
[tex]\[ -0.14 - (-0.04) = -0.10 \][/tex]
Given this consistent common difference, the answer is [tex]\( \boxed{-0.1} \)[/tex].
Thus, the common difference between successive terms in the sequence is [tex]\(-0.1\)[/tex].
1. Select Consecutive Terms: Choose the first two terms of the sequence for calculation, which are [tex]\(0.36\)[/tex] and [tex]\(0.26\)[/tex].
2. Calculate the Difference: Subtract the second term from the first term. The formula for the common difference [tex]\(\delta\)[/tex] is given by:
[tex]\[ \delta = \text{Next term} - \text{Previous term} \][/tex]
Specifically, here:
[tex]\[ \delta = 0.26 - 0.36 \][/tex]
3. Perform the Subtraction: Compute the value:
[tex]\[ \delta = 0.26 - 0.36 = -0.10 \][/tex]
4. Verify the Consistency: Optionally, you can check whether the difference is consistent between other successive terms to confirm it. For example:
[tex]\[ 0.16 - 0.26 = -0.10 \][/tex]
[tex]\[ 0.06 - 0.16 = -0.10 \][/tex]
[tex]\[ -0.04 - 0.06 = -0.10 \][/tex]
[tex]\[ -0.14 - (-0.04) = -0.10 \][/tex]
Given this consistent common difference, the answer is [tex]\( \boxed{-0.1} \)[/tex].
Thus, the common difference between successive terms in the sequence is [tex]\(-0.1\)[/tex].
