The sum of second and sixth terms of an arithmetic sequence is 4. The third term is 24 more than eleventh term. So determine the first three terms of the sequence.
a+d + a+5d = 4
a+2d = a+10d + 24
Collect terms and solve for a and d. Then write a,a+d,a+2d
14-3n
First three terms 11,8,5
I really don't understand this sequence... help plz
I do not understand
To solve this problem, let's first define the terms of the arithmetic sequence.
Let's assume that the first term of the sequence is "a," and the common difference between the terms is "d."
So, the terms of the arithmetic sequence can be written as:
First term: a
Second term: a + d
Third term: a + 2d
...
nth term: a + (n - 1)d
Now, let's use the given information to set up equations.
1. The sum of the second and sixth terms is 4:
(a + d) + (a + 5d) = 4
Simplifying:
2a + 6d = 4
2. The third term is 24 more than the eleventh term:
(a + 2d) = (a + 10d) + 24
Simplifying:
-8d = 24
d = -3
Now that we have found the value of the common difference (d), we can use it to find the value of the first term (a).
Plug the value of d back into equation (2):
-8d = 24
-8(-3) = 24
24 = 24
Since the equation is true, we have found the correct value for d.
Now, let's use the value of d to find a:
a = a + d
a = a + (-3)
0 = -3
This implies that a must be equal to zero.
So, the first term (a) of the arithmetic sequence is 0, the second term (a + d) is 0 + (-3) = -3, and the third term (a + 2d) is 0 + 2(-3) = -6.
Therefore, the first three terms of the sequence are 0, -3, -6.