If the first term of an AP is 6 and the fourth term is 12.
1) find the common difference
2) form the sequence
Nothing
just use your formulas ....
first term of an AP is 6 ---> a = 6
the fourth term is 12 ----> a + 3d = 12
6 + 3d = 12
your turn....
To find the common difference of an arithmetic progression (AP), you can subtract the first term from the second term (or any other consecutive terms). In this case, subtracting the first term from the fourth term will give you the common difference.
1) Common Difference:
d = 12 - 6
d = 6
Therefore, the common difference of this AP is 6.
2) Form the Sequence:
The formula to find the nth term of an arithmetic progression is given by:
a_n = a + (n-1)d
Where:
a_n = nth term
a = first term
d = common difference
n = position of the term in the sequence
Using this formula, we can find the terms of the sequence:
a_1 = a + (1-1)d
a_1 = 6 + (1-1)6
a_1 = 6
a_2 = a + (2-1)d
a_2 = 6 + (2-1)6
a_2 = 6 + 6
a_2 = 12
a_3 = a + (3-1)d
a_3 = 6 + (3-1)6
a_3 = 6 + 12
a_3 = 18
a_4 = a + (4-1)d
a_4 = 6 + (4-1)6
a_4 = 6 + 18
a_4 = 24
Therefore, the sequence formed by this arithmetic progression is 6, 12, 18, and 24.