the third of an arithmetic sequence is 14 and the ninth tern is -1. Find the first four terms of the sequence.
by definition:
a+2d = 14
a+8d = -1
subtract ...
6d = -15
d= -5/2
then
a+2(-5/2) = 14
a = 19
first 4 terms are
19, 33/2 , 14 , 23/2
a + 2d =14, a + 8d = -1. Solve simultaneously. . . .a =19 . .d =-5/2. .0. The sequence is . 19,16.5,14,11.5
To find the first four terms of an arithmetic sequence, we need to determine the common difference (d) and then use that to calculate each term.
Let's start by finding the common difference:
Given that the third term (a3) is 14 and the ninth term (a9) is -1, we can use the formula:
a9 = a3 + (9 - 3)d
Substituting the known values:
-1 = 14 + 6d
Now, let's solve this equation to find the value of d:
-1 - 14 = 6d
-15 = 6d
d = -15/6
d = -2.5
We have found that the common difference (d) is -2.5.
Now, we can calculate the first four terms of the arithmetic sequence:
The formula to find the nth term (an) of an arithmetic sequence is:
an = a1 + (n - 1)d
Substituting the values:
a1 = ?
n = 1
d = -2.5
a1 = a1 + (1 - 1)(-2.5)
a1 = a1 + 0
a1 = a1
As we can see, there is no specific value for the first term (a1). It could be any real number.
However, we can determine the second, third, and fourth terms using the common difference (d):
a2 = a1 + (2 - 1)d
= a1 + (1)(-2.5)
= a1 - 2.5
a3 = a1 + (3 - 1)d
= a1 + (2)(-2.5)
= a1 - 5
a4 = a1 + (4 - 1)d
= a1 + (3)(-2.5)
= a1 - 7.5
So, the first four terms of the arithmetic sequence are:
a1, a1 - 2.5, a1 - 5, a1 - 7.5
However, since the value of a1 is unknown, we cannot determine the exact values of the first four terms without additional information.