If the first term of an AP is 6 and the forth term is 12 find common difference
the two items are three terms apart, so
3d = 12-6
d = 2
To find the common difference of an arithmetic progression (AP), we can use the formula for the nth term of an AP:
aₙ = a₁ + (n - 1)d
Where:
aₙ is the nth term of the AP
a₁ is the first term of the AP
d is the common difference
n is the position of the term in the AP
Given that the first term (a₁) is 6 and the fourth term (a₄) is 12, we can substitute these values into the formula:
a₄ = a₁ + (4 - 1)d
12 = 6 + 3d
Now we can solve this equation for d:
12 - 6 = 3d
6 = 3d
Dividing both sides by 3:
d = 2
Therefore, the common difference (d) is 2.
To find the common difference (d) of an arithmetic progression (AP), you can use the formula:
Term_n = First_term + (n-1) * d
Given that the first term (Term_1) is 6 and the fourth term (Term_4) is 12, we can substitute the values into the formula:
Term_4 = First_term + (4-1) * d
12 = 6 + (3*d)
Now, let's solve the equation for d:
12 - 6 = 3d
6 = 3d
Dividing both sides by 3:
6/3 = d
The common difference (d) of the arithmetic progression is 2.