Answer:
The expression that represents the given sequence is 5+6(n-1). Option C (not labeled).
Explanation:
<u>Arithmetic Sequences</u>
In an arithmetic sequence, each term can be obtained by adding or subtracting a fixed number to the previous term. That fixed number is called the common difference.
We are given the following sequence:
5, 11, 17, 23, 29, ...
Each term is located in a position starting from n=1. Let's test each option:
A For n=1 we should have the first term (5). Substituting n=1 into the general equation: 5+6(n+1) = 5+6(1+1) = 5+12 = 17. Since the resulting term is not 5, this option is incorrect.
B For n=1, 6+5(n+1)= 6+5(2)=16. This option is incorrect.
C (not labeled) For n=1, 5+6(n-1)=5+6(1-1)=5+0=5. The first term is correct. Let's test for the second term (n=2):
5+6(2-1)=5+6=11. Correct. For n=3
5+6(3-1)=5+12=17. Correct.
We can see the terms are increasing by 6, and the given sequence is also increasing by 6. Thus, This option is correct.
D For n=1, 6+5 (n-1)=6+0=6. This option is incorrect.
The smallest number would be 4
the three numbers would be 4, 10, and 14, which would have a sum of 28
Answer:
sin(θ) = 24/25
Step-by-step explanation:
We can easily solve this problem by applying the trigonometric identity
sin(x) ^2 + cos(x) ^2 = 1
In this case
sin(θ) ^2 + cos(θ) ^2 = 1
sin(θ) ^2 = 1 - cos(θ) ^2
sin(θ) ^2 = 1 - (7/25) ^2
sin(θ) ^2 = 1 - (49/625)
sin(θ) ^2 = 576/625
sin(θ) = √( 576/625)
sin(θ) = 24/25
