the second and sixth terms of an arithmetic sequence is 4. the third term is 24more than the 11th term.
Determine the first three terms of the sequence
If the 2nd and 6th terms are equal, then they must all be the same.
Now, if you mean the sum is 4, then we have
a+d + a+5d = 4
a+2d = a+10d+24
Now solve for a and d and write the sequence.
To determine the first three terms of the arithmetic sequence, we can use the given information and the formulas for arithmetic sequences.
Let's denote the first term of the sequence as 'a', and the common difference between terms as 'd'.
Given:
The second term is 4.
The sixth term is 4.
From the formula for the nth term of an arithmetic sequence, we can write:
a + d = 4 ---(1)
a + 5d = 24 ---(2)
Since we have two equations with two variables, we can solve this system of equations.
Subtracting equation (1) from equation (2), we get:
5d - d = 24 - 4
4d = 20
d = 5
Now substitute the value of 'd' in equation (1):
a + 5 = 4
a = 4 - 5
a = -1
Therefore, the first term of the arithmetic sequence is -1.
To find the first three terms, substitute the values of 'a' and 'd' into the formula for the nth term:
First term = a = -1
Second term = a + d = -1 + 5 = 4
Third term = a + 2d = -1 + 2(5) = -1 + 10 = 9
Therefore, the first three terms of the arithmetic sequence are -1, 4, and 9.