The 28th term of an AP is -5, find it's common difference of it's first term is 31. a= first term, n= no. of terms, d= common difference, l= last term
we are told that a = 31, and that term(28) = a + 27d = -5
31 + 27d = -5
27d = -36
d -36/27 = -4/3
Well, first let me assure you that the common difference of the AP is not hiding in your closet or under your bed. It's a mathematical concept related to Arithmetic Progressions. But don't worry, I'll help you find it!
We know that the first term (a) is 31. So, a = 31. The 28th term (l) is -5. So, l = -5.
The formula to find the nth term of an Arithmetic Progression (AP) is:
a + (n - 1)d = l
Plugging in the values we know, we get:
31 + (28 - 1)d = -5
Now we can do some mathematical circus tricks to find the common difference (d):
31 + 27d = -5
Subtracting 31 from both sides, we get:
27d = -5 - 31
That simplifies to:
27d = -36
Finally, dividing both sides by 27:
d = -36 / 27
So, the common difference (d) of the AP is approximately -1.333.
Remember, math is serious business, but that doesn't mean we can't have a little fun along the way!
To find the common difference, we can use the formula for the nth term of an arithmetic progression (AP):
ln = a + (n-1)d
We are given n = 28 and the 28th term, ln, is -5. We are also given the first term, a, as 31.
Substituting the given values into the formula, we have:
-5 = 31 + (28-1)d
Simplifying the equation gives:
-5 = 31 + 27d
Rearranging the equation to isolate d:
27d = -5 - 31
27d = -36
Dividing both sides of the equation by 27:
d = -36/27
Simplifying the fraction:
d = -4/3
Therefore, the common difference of the arithmetic progression is -4/3.
To find the common difference (d) of an arithmetic progression (AP), we need to know the first term (a) and the last term (l).
Given:
a = 31 (first term)
l = -5 (28th term)
We can use the formula for the nth term of an AP to find the common difference (d). The formula is:
l = a + (n - 1)d
Substituting the given values into the formula:
-5 = 31 + (28 - 1)d
Simplifying the equation:
-5 = 31 + 27d
Rearranging the equation:
27d = -5 - 31
27d = -36
Dividing both sides of the equation by 27:
d = -36/27
Simplifying the fraction:
d = -4/3
Therefore, the common difference (d) of the given AP is -4/3.