3. Write an explicit formula for the sequence 10, 95, 9, 85, 8, Then find a_{4} (1 point)
a_{n} - 10 + 0.5(n - 1) a_{4} = 7.5
a_{2} - 10 + 5(n - 1) . a * -6.5
a_{2} - 10 - 5(n - 1) a_{i} - 6
a_{2} - 10 - 5(n - 1) a_{2} - 6.5
To find the explicit formula for the given sequence, we need to analyze the pattern in the sequence. Looking at the sequence, we can see that it alternates between two types of numbers - one with a constant difference of 5, and the other with a constant difference of -10.
Let's break down the sequence into two separate sequences:
Sequence A: 10, 9, 8, ...
Sequence B: 95, 85, ...
For Sequence A, we can see that each term is obtained by subtracting 1 from the previous term. So the explicit formula for Sequence A can be written as:
a(n) = 10 - (n - 1)
For Sequence B, we can see that each term is obtained by subtracting 10 from the previous term. However, the sequence starts with 95, which is not obtained by subtracting 10 from the previous term. So we need to adjust our formula to account for this.
To adjust the formula, we can rewrite it as:
a(n) = 85 - (n - 2) * 10
Note: Since the first term of Sequence B is obtained by subtracting 10 from the first term of Sequence A, we need to subtract 2 from n instead of 1 in the formula.
Now, to find a4 (the fourth term of the sequence), we can substitute n = 4 into the appropriate formula.
For Sequence A (a), substituting n = 4:
a(4) = 10 - (4 - 1)
= 10 - 3
= 7
For Sequence B (b), substituting n = 4:
b(4) = 85 - (4 - 2) * 10
= 85 - 2 * 10
= 85 - 20
= 65
The fourth term of the sequence is obtained by alternating between the terms of Sequence A and Sequence B.
Therefore, a4 = 7, 65.