Question

In an AP an=4n-2then the common difference

Answer 1

Step-by-step explanation:

an = 4n - 2

let n=1

a1 = 4(1) - 2

= 4-2

= 2

let n=2

a2 = 4(2)-2

= 8-2

= 6

d = a2-a1

= 6-2

= 4

Answer 2

Given:      

In an arithmetic progression, the value of the nth term is 4n - 2.    

To Find:      

The common difference of the given A.P is?  

Solution:    

1. Consider an A.P having n terms with the first term a, common difference d. The nth term of the A.P is given by the formula,      

=> nth term of an A.P = Tn = a + (n-1)d,      

2. The first term of the A.P is,  

=> a1 = a = 4(1) - 2,  

=> a1 = a = 2,  

=> a = 2. ( First term = 2 )  

3. The value of the second term of the A.P is,  

=> a2 = a + d = 4(2) - 2,  

=> a2 = a + d = 6,  

=> a + d = 6, ( Assume as equation 1 ).

4. Substitute the value of a in equation 1,

=> a + d = 6,

=> 2 + d = 6,

=> d= 6 - 2,

=> d = 4.

=> Common difference = 4.

Therefore, the value of the common difference (d) is 4.