Answer:
We conclude that the recursive formula would be:
aₙ = aₙ₋₁ + 4
Step-by-step explanation:
Given the sequence
14, 18, 22, 26, 30, .
Determining the common difference between the adjacent terms
18-4 = 22, 22-18 = 4, 26-22 = 4, 30-26 = 4
As the common difference is same.
i.e. d = 4
Thus, this sequence represents the Arithmetic sequence.
also
a₁=14
As the common difference d=4, meaning the next term (aₙ₋₁) can be obtained by adding 4 to the previous term.
Thus, the recursive formula would be:
aₙ = aₙ₋₁ + 4
VERIFICATION
Given
a₁=14
Put n = 2 to get the next term i.e. (a₂).
Using the recursive formula
aₙ = aₙ₋₁ + 4
a₂ = a₂₋₁ + 4
= a₁ + 4
= 14 + 4
= 18
Thus, a₂ = 18 can be obtained by adding 4 to the previous term.
Therefore, we conclude that the recursive formula would be:
aₙ = aₙ₋₁ + 4
