Find an explicit rule for the nth term of the sequence.
7, -7, 7, -7, (5 points)
select one:
a. an = 7 • (-1)n-1
b. an = 7 • (-1)n
c. an = 7 • 1n-1
d. an = 7 • 1n+1

(a) The ONLY explicit rule for the nth term of the sequence is .

Step-by-step explanation:

Here, the given sequence is 7, -7, 7, -7, ...

The first term = 7, Second term = -7, Third term =-7 and so on..

Now check the given sequence for each given formula, we get:

(1)  

Now, for n = 1 :

Similarly, for, n = 2:  

Hence, the given formula satisfies the given sequence.

(2)  

Now, for n = 1 :

But, First term = 7

Hence, the given formula DO NOT satisfy the given sequence.

(3)  

Now, for n = 1 :

Similarly, for, n = 2:  

But, Second term = -7

Hence, the given formula DO NOT satisfy the given sequence.

(4)

Now, for n = 1 :

Similarly, for, n = 2:  

But, Second term = -7

Hence, the given formula DO NOT satisfy the given sequence.

So, the ONLY explicit rule for the nth term of the sequence is .

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2