Question

Write a recursive definition for the sequence 14, 10, 6, 2...
a. a1=14, an=an-1+4
b. a1=2, an=an-1-4
c. a1=2,an=an-1+4
d. a1=14,an=an-1-4

Answer 1

The answer is:

d. $a_{1}=14,$ $a_{n}=a_{n-1}-4$

Answer 2

Recursive definition for the given sequence is a₁ =14 , aₙ = aₙ₋₁ - 4.

What is recursive sequence?

" Recursive sequence is sequence in which  terms are defined with the help of one or more than one previous given terms."

Formula used

aₙ =aₙ₋₁ + d

d = aₙ - aₙ₋₁

According to the question,

a₁ = 14

a₂ =10

a₃ =6

a₄ = 2

Therefore,

d = a₂ -a₁

  = 10 - 14

  = - 4

Substitute the value of d in the recursive formula we get,

aₙ = aₙ₋₁ + (-4)

aₙ =aₙ₋₁ -4

Hence, recursive definition for the given sequence is a₁ =14 , aₙ = aₙ₋₁ - 4.

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