The 18th term of an ap is 25.find it's first term if it's common difference is 2
To find the first term of an arithmetic progression (AP) given the 18th term and the common difference, you can use the formula for the nth term of an AP.
The formula for the nth term of an AP is:
nth term = first term + (n-1) * common difference
Let's substitute the given values into the formula:
25 = first term + (18-1) * 2
25 = first term + 17 * 2
25 = first term + 34
Subtracting 34 from both sides, we get:
25 - 34 = first term + 34 - 34
-9 = first term
Therefore, the first term of the AP is -9.
To find the first term of an arithmetic progression (AP), we can use the formula:
\[ a_n = a + (n-1) \cdot d \]
Where:
- \(a_n\) is the \(n\)th term of the AP,
- \(a\) is the first term of the AP,
- \(n\) is the term number,
- \(d\) is the common difference of the AP.
Given that the 18th term of the AP is 25 and the common difference is 2, we can substitute these values into the formula and solve for \(a\):
\[ 25 = a + (18-1) \cdot 2 \]
Simplifying the equation:
\[ 25 = a + 17 \cdot 2 \]
\[ 25 = a + 34 \]
\[ a = 25 - 34 \]
\[ a = -9 \]
Therefore, the first term of the AP is -9.
To find the first term of an arithmetic progression (AP), we can use the formula for the nth term of an AP:
๐กโ = ๐ + (๐ - 1)๐
where:
- ๐กโ is the nth term of the AP,
- ๐ is the first term of the AP, and
- ๐ is the common difference of the AP.
Given that the 18th term (๐กโโ) of the AP is 25 and the common difference (๐) is 2, we can substitute these values into the formula to find the first term (๐).
25 = ๐ + (18 - 1)(2)
Simplifying the equation:
25 = ๐ + 17(2)
25 = ๐ + 34
Subtracting 34 from both sides:
๐ = 25 - 34
๐ = -9
Therefore, the first term of the arithmetic progression is -9.