The 28th term of an AP is-5.Find its common difference if its first term is 31

Answer 1

Let's denote the common difference of the arithmetic progression as "d" and the first term as "a1".
We know that the formula for the nth term of an arithmetic progression is:
an = a1 + (n-1)d
We are given that a28 = -5, a1 = 31, and n = 28. Plugging these values into the formula, we get:
-5 = 31 + (28-1)d
Simplifying, we get:
-5 = 31 + 27d
Subtracting 31 from both sides, we get:
-36 = 27d
Dividing both sides by 27, we get:
d = -36/27
Simplifying, we get:
d = -4/3
Therefore, the common difference of the arithmetic progression is -4/3.