A prism's volume is the area of the face that does not have more than 1 equal counterpart mulitplied by the height of the entire prism, in which the height of the prism is not any of the sidelengths of the face whose area is being multiplied.

7 0

3 years ago

Write a recursive rule and an explicit rule for the sequence 3,7,11,15

m_a_m_a [10]

Answer:

The Recursive formula for the sequence is:

aₙ = aₙ₋₁ + d

The Explicit formula for the sequence is:

$a_n=4n-1$

Step-by-step explanation:

Given the sequence

3,7,11,15

Here:

a₁ = 3

computing the differences of all the adjacent terms

7 - 3 = 4, 11 - 7 = 4, 15 - 11 = 4

The difference between all the adjacent terms is the same and equal to

d = 4

We know that a recursive formula basically defines each term of a sequence using the previous term(s).

The recursive formula of the Arithmetic sequence always involves the first term.

a₁ = 3

We know that, in the Arithmetic sequence, every next term can be obtained by adding the common difference and the preceding term.

The recursive formula of the sequence is:

aₙ = aₙ₋₁ + d

substitute n = 2 to find the 2nd term

a₂ = a₂₋₁ + d

a₂ = a₁+ d

substitute a₁ = 3 and d = 4

a₂ = 3 + 4

a₂ = 7

Thus, the recursive formula for the sequence 3,7,11,15 is:

aₙ = aₙ₋₁ + d

An explicit rule for the sequence

Given the sequence

3,7,11,15

We already know that

a₁ = 3

d = 4

An arithmetic sequence has a constant difference 'd' and is defined by

$a_n=a_1+\left(n-1\right)d$

substituting a₁ = 3 and d = 4

$a_n=4\left(n-1\right)+3$

$a_n=4n-4+3$

$a_n=4n-1$

Therefore, an explicit rule for the sequence

$a_n=4n-1$

6 0

3 years ago