Find the first four terms of the sequence given by the following.
4,=(-1)".31%, n=1, 2, 3, ...

The first term of the sequence is:

Step-by-step explanation:

Given the sequence

aₙ = (-1)ⁿ · 3n²

substituting n = 1 to determine the first term

a₁ = (-1)¹ · 3(1)²

a₁ = (-1)¹ · 3(1)²

Applying the exponent rule:

a₁ = -1 · 3(1)

a₁ = -1 · 3

a₁ = -3

substituting n = 2 to determine the 2nd term

a₂ = (-1)² · 3(2)²

a₂ = 1 · 3(4)

a₂ = 12

substituting n = 3 to determine the 3rd term

a₃ = (-1)³ · 3(3)²

a₃ = -1 · 3(9)

a₃ = -1 · 27

a₃ = -27

substituting n = 4 to determine the 4th term

a₄ =  (-1)⁴ · 3(4)²

a₄ = 1 · 3(16)

a₄ = 1 · 48

a₄ = 48

Therefore, the first term of the sequence is:

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".