Question

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

Answer 1

an=7•(-1)^n-1

Explanation:

Answer 2

(a) The ONLY explicit rule for the nth term of the sequence is
`a_n = 7  * (-1)^(n-1)\\`.

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)
`a_n = 7  * (-1)^(n-1)\\`

Now, for n = 1 :
`a_1 = 7  * (-1)^(1-1)\\`

`= 7 * (-1)^0 =  7 * 1 = 7 \implies a_1 = 7`

Similarly, for, n = 2:
`a_2 = 7  * (-1)^(2-1)\\`

`= 7 * (-1)^1 =  7 * (-1) = -7 \implies a_2 = -7`

Hence, the given formula satisfies the given sequence.

(2)
`a_n = 7  * (-1)^(n)\\`

Now, for n = 1 :
`a_1 = 7  * (-1)^(1)\\`

`= 7 * (-1)^1 =  7 * (-1) = -7 \implies a_1 = -7`

But, First term = 7

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

(3)
`a_n = 7  * (1)^(n-1)\\`

Now, for n = 1 :
`a_1 = 7  * (1)^(1-1)\\`

`= 7 * (1)^0 =  7 * 1 = 7 \implies a_1 = 7`

Similarly, for, n = 2:
`a_2 = 7  * (1)^(2-1)\\`

`= 7 * (1)^1 =  7 * (1) = 7 \implies a_2 = 7`

But, Second term = -7

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

(4)
`a_n = 7  * (1)^(n+1)\\`

Now, for n = 1 :
`a_1 = 7  * (1)^(1+1)\\`

`= 7 * (1)^2 =  7 * 1 = 7 \implies a_1 = 7`

Similarly, for, n = 2:
`a_2 = 7  * (1)^(2+1)\\`

`= 7 * (1)^3 =  7 * (1) = 7 \implies a_2 = 7`

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
`a_n = 7  * (-1)^(n-1)\\`.