Absolutely!
To find the first term and the common difference of the arithmetic progression (A.P.) given by the sequence [tex]\(0.6, 1.7, 2.8, 3.9, \ldots\)[/tex], let's break it down step by step.
### Step 1: Identify the First Term
The first term of the arithmetic progression (A.P.) is simply the first number in the sequence.
So, the first term is:
[tex]\[ a_1 = 0.6 \][/tex]
### Step 2: Determine the Common Difference
The common difference in an arithmetic progression is found by subtracting the first term from the second term. The sequence provided is [tex]\(0.6, 1.7, 2.8, 3.9, \ldots\)[/tex].
The common difference [tex]\(d\)[/tex] is calculated as follows:
[tex]\[ d = a_2 - a_1 \][/tex]
Where [tex]\(a_2\)[/tex] is the second term and [tex]\(a_1\)[/tex] is the first term. Substituting the terms from the sequence:
[tex]\[ d = 1.7 - 0.6 \][/tex]
[tex]\[ d = 1.1 \][/tex]
### Summarizing the Results
Therefore, for the arithmetic progression given by the sequence [tex]\(0.6, 1.7, 2.8, 3.9, \ldots\)[/tex]:
- The first term [tex]\(a_1\)[/tex] is [tex]\(0.6\)[/tex].
- The common difference [tex]\(d\)[/tex] is [tex]\(1.1\)[/tex].
So, the first term and the common difference of the given A.P. are [tex]\(0.6\)[/tex] and [tex]\(1.1\)[/tex] respectively.
