If the First Term Of An Ap is 6 and The Fourth Term Is 12.find The Common Difference And Form The Sequence
a4 = a1 + 3d
so, 3d = 12-6 = 6
d = 2
6,8,10,12,...
To find the common difference and form the sequence, we can use the formula for the nth term of an arithmetic progression (AP):
An = a + (n - 1)d
Where:
An represents the nth term
a represents the first term
n represents the position of the term
d represents the common difference
Given:
The first term (a) is 6
The fourth term (A4) is 12
We know that A4 = a + (4 - 1)d
Substituting the given values, we have:
12 = 6 + 3d
Now, let's solve for d:
12 - 6 = 3d
6 = 3d
d = 2
Therefore, the common difference (d) is 2.
To form the sequence, we can substitute the values of the common difference into the formula for the nth term of an AP:
An = 6 + (n - 1)2
Using this formula, we can calculate any term in the sequence. Let's find the first six terms:
A1 = 6 + (1 - 1)2 = 6
A2 = 6 + (2 - 1)2 = 8
A3 = 6 + (3 - 1)2 = 10
A4 = 6 + (4 - 1)2 = 12
A5 = 6 + (5 - 1)2 = 14
A6 = 6 + (6 - 1)2 = 16
Therefore, the sequence formed by this AP is: 6, 8, 10, 12, 14, 16.