-6 is given as a fourth term,-34 is a eleventh term what are the first three terms?can i solve it simultaneously
Are you talking about a sequence?
If so is it arithmetic?
is it geometric?
or what
To find the first three terms of the sequence, we can use the formula for the nth term of an arithmetic sequence, which is:
an = a1 + (n-1)d
where:
an = nth term
a1 = first term
n = number of terms
d = common difference
Given that the fourth term is -6 (a4 = -6) and the eleventh term is -34 (a11 = -34), we can set up two equations:
-6 = a1 + (4-1)d
-34 = a1 + (11-1)d
We can now solve these two equations simultaneously to find the values of a1 and d.
From the first equation:
-6 = a1 + 3d
From the second equation:
-34 = a1 + 10d
To solve these equations simultaneously, we can subtract the first equation from the second equation:
-34 - (-6) = (a1 + 10d) - (a1 + 3d)
-34 + 6 = a1 + 10d - a1 - 3d
-28 = 7d
Dividing both sides by 7:
d = -4
Now that we have the value of d, we can substitute it back into one of the original equations to find a1:
-6 = a1 + 3(-4)
-6 = a1 - 12
a1 = 6 - 12
a1 = -6
Therefore, the first three terms of the sequence are -6, -10, and -14.
To find the first three terms in this arithmetic sequence, we can start by determining the common difference between consecutive terms. Once we have the common difference, we can work backwards to find the first three terms.
Let's denote the first term as "a" and the common difference as "d".
We are given that the fourth term is -6, which means:
a + 3d = -6 (equation 1)
We are also given that the eleventh term is -34:
a + 10d = -34 (equation 2)
To solve these two equations simultaneously, we can use the method of substitution or elimination.
Method 1: Substitution
Solve equation 1 for "a" and substitute it into equation 2:
a = -6 - 3d
Substitute:
(-6 - 3d) + 10d = -34
Simplify:
4d = -28
Divide by 4:
d = -7
Now substitute the value of "d" back into equation 1 to find "a":
a + 3(-7) = -6
a - 21 = -6
a = 15
So, the first term (a) is 15 and the common difference (d) is -7.
To find the first three terms, use the formula for the nth term of an arithmetic sequence:
nth term = a + (n - 1)d
For n = 1:
First term = a = 15
For n = 2:
Second term = a + (2 - 1)d = 15 + (2 - 1)(-7) = 15 - 7 = 8
For n = 3:
Third term = a + (3 - 1)d = 15 + (3 - 1)(-7) = 15 - 14 = 1
Therefore, the first three terms in the given arithmetic sequence are:
15, 8, 1.