Answer:
First three terms = 28, 22, and 16
Explanation:
The formula for the nth term of an arithmetic sequence is given by:
an = a1 + (n-1)d, where:
- an is the nth term,
- a1 is the first term,
- n is the term position (e.g., 1st, 4th, etc.),
- and d is the common difference.
Step 1: Find a1:
We can find a1 by substituting 10 for an, 4 for n, and -6 for d in the nth term formula:
10 = a1 + (4 - 1) * -6
10 = a1 + 3 * -6
(10 = a1 - 18) + 18
28 = a1
Thus, the first term is 28.
Step 2: Find a2 (the second term):
Now, we can find the second term by substituting 28 for a1, 2 for n, and -6 for d in the nth term formula:
a2 = 28 + (2 - 1) * -6
a2 = 28 + 1 * -6
a2 = 28 - 6
a2 = 22
Thus, the second term is 22.
Step 3: Find a3 (the third term):
Now, we can find the third term by substituting 28 for a2, 3 for n, and -6 for d in the nth term formula:
a3 = 28 + (3 - 1) * -6
a3 = 28 + 2 * -6
a3 = 28 - 12
a3 = 16
Thus, the third term is 16.
Step 4: Write the first three terms:
Therefore, the first three terms of the arithmetic series are 28, 22, and 16.