Question

Write an explicit formula for An; the nth term of the sequence 33, 43, 53,..

Answer 1

`a_(n)` = 10n + 23

Explanation:

there is a common difference between consecutive terms in the sequence, that is

43 - 33 = 53 - 43 = 10

this indicates the sequence is arithmetic with explicit formula

`a_(n)` = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 33 and d = 10 , then the explicit formula is

`a_(n)` = 33 + 10(n - 1) = 33 + 10n - 10 = 10n + 23