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aksik [14]
2 years ago
14

Write a word phrase that can represent the algebraic expression: 2(5-n)

Mathematics
1 answer:
Fed [463]2 years ago
3 0
2(5-n) can be an expression of "twice the difference of 5 and n".
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Write a recursive rule and an explicit rule for the<br> sequence<br> 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.

so

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

<u>An explicit rule for the sequence</u>

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
2 years ago
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