In an A.P.the third term is four times the first term, and the sixth term is 17; find the series.
a+2d = 4a ---> 2d = 3a ----> a = 2d/3
sub that into
a+5d = 17
2d/3 + 5d = 17
17d/3 = 17
d = 3
then a = (2/3)(3) = 2
You don't specify how many terms you want in the series, but you should know the formula
Now that we know a and d, it is easy
To find the series in an Arithmetic Progression (AP), we need to determine the common difference (d) and the first term (a).
Given:
The third term is four times the first term.
The sixth term is 17.
Step 1: Finding the common difference (d)
Since the third term is four times the first term, we can express this as:
a + 2d = 4a
By simplifying:
2d = 3a
d = (3/2)a
Step 2: Finding the first term (a)
Since the sixth term is 17, we can express this as:
a + 5d = 17
Substituting the value of d from Step 1:
a + 5((3/2)a) = 17
a + (15/2)a = 17
(17/2)a = 17
a = 2
Step 3: Finding the common difference (d)
Substituting the value of a from Step 2 into the equation in Step 1:
d = (3/2)(2)
d = 3
Therefore, the first term is 2 and the common difference is 3.
The series in the Arithmetic Progression is:
2, 5, 8, 11, 14, 17