Determine the first three terms of the arithmetic sequence of which the 4th term is -13 and the 7th term is -25.
common difference ... d = (-25 - 13) / (7 - 4)
3rd = 4th - d ... 2nd = 3rd - d ... 1st = 2nd - d
To determine the first three terms of an arithmetic sequence, we need to find the common difference (d) and then use it to calculate the terms.
Step 1: Find the common difference (d).
To find the common difference (d), we subtract the 4th term from the 7th term:
-25 - (-13) = -25 + 13 = -12
So, the common difference (d) is -12.
Step 2: Calculate the first term (a).
To find the first term (a), we can use the formula:
a = 4th term - (3 * d)
Substituting in the values we have:
a = -13 - (3 * -12)
a = -13 + 36
a = 23
So, the first term (a) is 23.
Step 3: Calculate the second term (a + d).
To find the second term, we can use the formula:
2nd term = first term + d
Substituting in the values we have:
2nd term = 23 + (-12)
2nd term = 23 - 12
2nd term = 11
So, the second term is 11.
Step 4: Calculate the third term (a + 2d).
To find the third term, we can use the formula:
3rd term = first term + 2d
Substituting in the values we have:
3rd term = 23 + 2(-12)
3rd term = 23 - 24
3rd term = -1
So, the third term is -1.
Therefore, the first three terms of the arithmetic sequence are 23, 11, and -1.
To determine the first three terms of an arithmetic sequence, we need to find the common difference (d) and then use it to find each term in the sequence.
Step 1: Finding the common difference (d)
The common difference between consecutive terms in an arithmetic sequence remains constant. We can find it by subtracting any two consecutive terms.
Given that the 4th term is -13 and the 7th term is -25, let's subtract the two values to find the common difference:
-25 - (-13) = -25 + 13 = -12
Therefore, the common difference (d) is -12.
Step 2: Finding the first three terms
To determine the first term (a), we can use the formula: a = nth term - (n-1) * d.
Let's start with the 4th term and use it as a reference to find the first term:
a = -13 - (4 - 1) * (-12)
a = -13 - 3 * (-12)
a = -13 + 36
a = 23
Now we can find the second term (a2) by adding the common difference to the first term:
a2 = a + d
a2 = 23 + (-12)
a2 = 11
Finally, we find the third term (a3) by adding the common difference to the second term:
a3 = a2 + d
a3 = 11 + (-12)
a3 = -1
Therefore, the first three terms of the arithmetic sequence are:
a1 = 23
a2 = 11
a3 = -1