Find the second, fourth, and eleventh terms of the
sequence described by each explicit formula.

a(n) = -9 + (n - 1)(3)

The second term is -6 , the fourth term is 0 , the eleventh term is 21

Step-by-step explanation:

* Lets revise the explicit formula

- An explicit formula will create a sequence using n, the number

 position of each term.

- If you can find an explicit formula for a sequence, you will be able

 to quickly and easily find any term in the sequence by replacing

 n with the number of the term you want

- It defines the sequence as a formula in terms of n.

* Now lets solve the problem

- The formula of the sequence is A(n) = -9 + (n - 1)(3)

- A(n) is any term in the sequence

- n is the position of the number

- To find the second term put n = 2

∵ n = 2

∴ A(2) = -9 + (2 - 1)(3) = -9 + (1)(3) = -9 + 3 = -6

* The second term is -6

- To find the fourth term put n = 4

∵ n = 4

∴ A(4) = -9 + (4 - 1)(3) = -9 + (3)(3) = -9 + 9 = 0

* The fourth term is 0

- To find the eleventh term put n = 11

∵ n = 11

∴ A(11) = -9 + (11 - 1)(3) = -9 + (10)(3) = -9 + 30 = 21

* The eleventh term is 21

Second term = -6

Fourth term = 0

Eleventh term = 21

Step-by-step explanation:

We are given the following explicit formula of an arithmetic sequence and we are to find the second, fourth and the eleventh terms of this sequence:

where = nth term, and = number of term.

Second term = -6

Fourth term = 0

Eleventh term = 21

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

560

step-by-step explanation:

giggidy