The 128th terms of a AP is -5 find its common difference of its first term is 31
Let's use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
We are given that a128 = -5, a1 = 31, and n = 128. We need to find d.
Using the formula, we can substitute the given values: -5 = 31 + (128-1)d.
Simplifying the equation, we have: -5 = 31 + 127d.
Subtracting 31 from both sides, we get: -36 = 127d.
Dividing by 127, we find: d ≈ -0.2835.
Therefore, the common difference of the arithmetic sequence is approximately -0.2835.
To find the common difference of an arithmetic progression (AP) given the first term and any term in the series, we can use the formula:
nth term = first term + (n - 1) * common difference
In this case, we know that the 128th term is -5, and the first term is 31. Let's substitute these values into the formula and solve for the common difference.
-5 = 31 + (128 - 1) * common difference
Simplifying the equation:
-5 = 31 + 127 * common difference
Rearranging the terms:
127 * common difference = -36
Dividing both sides of the equation by 127:
common difference = -36 / 127
Thus, the common difference of the arithmetic progression is approximately -0.2835.
To find the common difference of an arithmetic progression (AP) when the first term is given, we can use the formula for the nth term of an AP:
An = A1 + (n - 1)d
where An represents the nth term, A1 is the first term, n is the term number, and d is the common difference.
In this case, we are given that the 128th term of the AP is -5 and the first term, A1, is 31. We want to find the common difference, d.
Let's substitute the given values into the formula and solve for d:
-5 = 31 + (128 - 1)d
Simplifying the equation:
-5 = 31 + 127d
Rearranging the equation:
127d = -5 - 31
127d = -36
Dividing both sides by 127:
d = -36 / 127
Therefore, the common difference of the arithmetic progression is approximately -0.283.