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Answer :
To find the tenth term of an arithmetic progression (AP), we need to understand a couple of important points.
1. In an AP, each term after the first is formed by adding a constant, called the common difference (denoted as [tex]\( d \)[/tex]), to the previous term.
2. The formula for the [tex]\( n \)[/tex]-th term of an AP is given by:
[tex]\[
a_n = a + (n-1) \cdot d
\][/tex]
where [tex]\( a \)[/tex] is the first term and [tex]\( n \)[/tex] is the term number.
Now, according to the problem:
- The first term [tex]\( a \)[/tex] is equal to [tex]\( 1 \frac{1}{2} \)[/tex] times the common difference [tex]\( d \)[/tex]. This can be written as:
[tex]\[
a = 1.5 \cdot d
\][/tex]
We need to find the tenth term of the sequence, which means [tex]\( n = 10 \)[/tex].
Substitute the values into the [tex]\( n \)[/tex]-th term formula:
- First, plug in the expression for [tex]\( a \)[/tex]:
[tex]\[
a_{10} = a + (10-1) \cdot d = 1.5d + 9d
\][/tex]
- Now, combine these terms to simplify:
[tex]\[
a_{10} = 1.5d + 9d = 10.5d
\][/tex]
Thus, the tenth term of the AP, expressed in terms of the common difference [tex]\( d \)[/tex], is [tex]\( 10.5d \)[/tex].
1. In an AP, each term after the first is formed by adding a constant, called the common difference (denoted as [tex]\( d \)[/tex]), to the previous term.
2. The formula for the [tex]\( n \)[/tex]-th term of an AP is given by:
[tex]\[
a_n = a + (n-1) \cdot d
\][/tex]
where [tex]\( a \)[/tex] is the first term and [tex]\( n \)[/tex] is the term number.
Now, according to the problem:
- The first term [tex]\( a \)[/tex] is equal to [tex]\( 1 \frac{1}{2} \)[/tex] times the common difference [tex]\( d \)[/tex]. This can be written as:
[tex]\[
a = 1.5 \cdot d
\][/tex]
We need to find the tenth term of the sequence, which means [tex]\( n = 10 \)[/tex].
Substitute the values into the [tex]\( n \)[/tex]-th term formula:
- First, plug in the expression for [tex]\( a \)[/tex]:
[tex]\[
a_{10} = a + (10-1) \cdot d = 1.5d + 9d
\][/tex]
- Now, combine these terms to simplify:
[tex]\[
a_{10} = 1.5d + 9d = 10.5d
\][/tex]
Thus, the tenth term of the AP, expressed in terms of the common difference [tex]\( d \)[/tex], is [tex]\( 10.5d \)[/tex].
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