A sequence can be generated using an + 1 = –0.25 + an, where a1 = 5 and n is a whole number greater than 1. What are the first 5 terms in the sequence?
To find the first 5 terms in the sequence, we can apply the given recursive formula.
a1 = 5
Applying the formula for a2:
a2 = -0.25 + a1 = -0.25 + 5 = 4.75
Applying the formula for a3:
a3 = -0.25 + a2 = -0.25 + 4.75 = 4.5
Applying the formula for a4:
a4 = -0.25 + a3 = -0.25 + 4.5 = 4.25
Applying the formula for a5:
a5 = -0.25 + a4 = -0.25 + 4.25 = 4
Therefore, the first 5 terms in the sequence are 5, 4.75, 4.5, 4.25, and 4.
To find the first five terms in the sequence, we can use the given formula: an + 1 = –0.25 + an.
Let's start by calculating the second term (a2) in the sequence.
Using the given formula, we substitute n = 1 and a1 = 5:
a2 = –0.25 + a1
= –0.25 + 5
= 4.75.
The second term, a2, is 4.75.
Now, let's calculate the third term (a3) in the sequence.
Using the formula again, we substitute n = 2 and a2 = 4.75:
a3 = –0.25 + a2
= –0.25 + 4.75
= 4.5.
The third term, a3, is 4.5.
Next, we can calculate the fourth term (a4) in the sequence.
Using the formula, we substitute n = 3 and a3 = 4.5:
a4 = –0.25 + a3
= –0.25 + 4.5
= 4.25.
The fourth term, a4, is 4.25.
Continuing this pattern, we can calculate the fifth term (a5) in the sequence.
Using the formula, we substitute n = 4 and a4 = 4.25:
a5 = –0.25 + a4
= –0.25 + 4.25
= 4.
The fifth term, a5, is 4.
Therefore, the first five terms in the sequence are: 5, 4.75, 4.5, 4.25, 4.