Question

Do you know number 11 to 13

Answer 1

see explanation

Explanation:

(11)

Note the differences in the values of the sequence

5 - 2 = 3

8 - 5 = 3

11 - 8 = 3

Since the differences are common then these are the terms of an arithmetic sequence with explicit formula

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference, thus

`a_(n)` = 2 + 3(n - 1) = 2 + 3n - 3 = 3n - 1 ← explicit formula

(12)

A recursive formula allows the next term in the sequence to be found from the previous term.

To obtain the next term add 3 to the previous term, thus

`a_(n+1)` =
`a_(n)` + 3 , with a₁ = 2

(13)

Using the explicit formula, then

`a_(20)` = (3 × 20) - 1 = 60 - 1 = 59