The 28th term of an Ap is -5. Find its common difference if the first term is 31
Given that the first term of the AP is 31 and the 28th term is -5, we need to find the common difference.
The formula to find the nth term of an arithmetic progression (AP) is:
an = a1 + (n-1)d
Where:
an = nth term
a1 = first term
d = common difference
In this case, we have:
a1 = 31
an = -5
n = 28
Plugging these values into the formula:
-5 = 31 + (28-1)d
-5 = 31 + 27d
-5 - 31 = 27d
-36 = 27d
Dividing both sides by 27:
-36/27 = 27d/27
-4/3 = d
So the common difference is -4/3.
To find the common difference (d) of an Arithmetic Progression (AP), we can use the following formula:
tn = a + (n - 1) * d
Where:
tn = nth term of the AP
a = first term
n = term number
Given:
The 28th term (tn) is -5
The first term (a) is 31
Using the formula, we can substitute the values and solve for d:
-5 = 31 + (28 - 1) * d
Simplifying the equation:
-5 = 31 + 27d
Rearranging terms:
27d = -5 - 31
27d = -36
Dividing by 27:
d = -36 / 27
Simplifying:
d = -4/3
Therefore, the common difference (d) of the AP is -4/3.
To find the common difference of an arithmetic progression (AP), you need information about at least two terms. Given that the 28th term is -5 and the first term is 31, we can use this information to find the common difference.
The formula to find the nth term (Tn) of an AP is given by:
Tn = a + (n - 1) * d
Where:
Tn = nth term
a = first term
n = term number
d = common difference
Using the information given, we can substitute the values into the formula:
-5 = 31 + (28 - 1) * d
Simplifying the equation:
-5 = 31 + 27d
To solve for d, we can isolate it on one side of the equation:
27d = -5 - 31
27d = -36
Dividing both sides of the equation by 27:
d = -36 / 27
d = -4/3
Therefore, the common difference of the arithmetic progression is -4/3.