What is the recursive formula for this sequence?
14, 18, 22, 26, 30, .

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

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

answer4 to the second power is 16

and 4 to the third power is 64,