Question

The 28th term of an ap is -5,find the common difference if the first term is 31​

Answer 1

Answer:

The common difference is -4/3.

Step-by-step explanation:

Recall that the direct formula for an arithmetic sequence is given by:

$\displaystyle x_n=a+d(n-1)$

Where n is the nth term, a is the initial term, and d is the common difference.

We are given that the first term a is 31.

We also know that the 28th term is -5. Hence, x₂₈ = -5. Substitute:

$\displaystyle x_{28}=-5=(31)+d(28-1)$

Solve for d. Simplify:

$-5=31+27d$

Thus:

$\displaystyle 27d=-36$

Divide both sides by 27. Hence, the common difference is:

$\displaystyle d=-\frac{36}{27}=-\frac{4}{3}$

Answer 2

Answer:

-4/3

Step-by-step explanation:

This question is equivalent to:

Find the slope of a line going through points (28,-5) and (1,31).

*Arithmetic sequences are linear. The common difference is the slope.

Any ways to find the slope line the points up and subtract vertically. Then put 2nd difference over 1st difference.

(28,-5)

(1,31)

---------subtracting

27, -36

So the slope or the common difference of this line or arithmetic sequence is -36/27. This reduces to -4/3.