Question

what is the common difference of a+1,a+2,a+3... and what is its algebraic form​

Answer 1

IF;

1, a+1=0 , a=(-1)

2, a+2=0 , a=(-2)

3, a+3 =0 ,a =(-3)

common difference :

The value of (a) in each eq^ is different

and value of (a) depends up on the

constant on that equation .

Answer 2

Step-by-step explanation:

Given :-

a+1,a+2,a+3...

To find :-

What is the common difference of a+1,a+2,a+3... and what is its algebraic form ?

Solution :-

Given sequence is a+1,a+2,a+3...

First term = a+1

Common difference = (a+2)-(a+1)

=> d = a+2-a-1

=> d = 1

and

d = (a+3)-(a+2)

=> d = a+3-a-2

=> d = 1

Common difference = 1

Since the common difference is same throughout the sequence.

So It is an Arithmetic Progression.

We know that

The nth term of an AP = an = a+(n-1)d

The nth term of the given AP

=> an = (a+1)+(n-1)(1)

=> an = a+1+n-1

=> an = a+n+(1-1)

=> an = a+n

Answer:-

The common difference of the given AP = 1

The algebraic form of the given AP is a+n

Used formulae:-

The nth term of an AP = an = a+(n-1)d