Question

The nth term of an A.P. is (2n-3).find the common difference.

Answer 1

Answer:

d=+2

Step-by-step explanation:

an=2n-3

let n be 1

a1= 2(1)-3

a1=2-3

a1=-1

let n be 2

a2=2(2)-3

a2=4-3

a2=1

let n be 3

a3=2(3)-3

a3=6-3

a3=3

d= a2-a1=a3-a2

1-(-1)=3-1

1+1=3-1

2=2

therefore d=+2

Answer 2

The common difference is 2

Explanation:

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers. If a1, a2, a3,..., and an are APs, the common difference "d" can be calculated as follows:

$D= (a_2 - a_1)=(a_3 - a_2)=(a_n - a_{n - 1})$

where "d" is common difference. It may be zero, negative, or positive.

Given $n^{th}$ term is $(2n-3)$

We know that the common difference in an AP is the difference between two consecutive terms.

So, the common difference can also be the difference between $(n+1)^{th}$ and  $n^{th}$ terms

$\therefore d=2(n+1)-3-(2n-3)\\\Rightarrow d=2n+2-3-2n+3\\\Rightarrow d=2$

So, the common difference of the AP is 2.

To learn more about common differences, click on the links below:

https://brainly.in/question/1331018?msp_srt_exp=5

https://brainly.in/question/24032359

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