The 43rd term of an AP is 26 find the first term of the progression,given its common difference 1/2
Let the first term of the arithmetic progression be 'a' and the common difference be 'd'.
The formula to find the nth term of an AP is:
an = a + (n-1)d
Given that the 43rd term of the AP is 26, we can substitute n = 43 and an = 26 into the formula to get:
26 = a + (43-1)(1/2)
26 = a + 42(1/2)
26 = a + 21
Subtracting 21 from both sides:
5 = a
Therefore, the first term of the arithmetic progression is 5.
To find the first term of an arithmetic progression (AP), we can use the formula:
\[ a_n = a_1 + (n-1)d \]
where:
- \(a_n\) is the \(n\)th term of the AP
- \(a_1\) is the first term of the AP
- \(d\) is the common difference
- \(n\) is the term number
In this case, we are given that the 43rd term of the AP is 26, and the common difference is \( \frac{1}{2} \). Let's use the formula to find \(a_1\):
\[ 26 = a_1 + (43-1) \left(\frac{1}{2}\right) \]
Simplifying the equation:
\[ 26 = a_1 + 42 \left(\frac{1}{2}\right) \]
\[ 26 = a_1 + 21 \]
Now, let's isolate \(a_1\):
\[ a_1 = 26 - 21 \]
\[ a_1 = 5 \]
Therefore, the first term of the arithmetic progression is 5.
To find the first term of an arithmetic progression (AP), we can use the formula:
nth term = first term + (n - 1) * common difference
Here, the given information is the 43rd term of the AP, which is 26, and the common difference is 1/2.
Let's substitute these values into the formula:
26 = first term + (43 - 1) * (1/2)
To simplify, we'll calculate (43 - 1) * (1/2):
42 * (1/2) = 21
The equation now becomes:
26 = first term + 21
To isolate the first term, we'll subtract 21 from both sides of the equation:
26 - 21 = first term
5 = first term
Therefore, the first term of the AP is 5.