Question

Write an
explicit formula for An, the nth term of the sequence 20, 30, 40, ....

Answer 1

`A_(n)` = 10n + 10

Explanation:

There is a common difference between consecutive terms in the sequence

d = 30 - 20 = 40 - 30 = 10

This indicates the sequence is arithmetic with explicit formula

`A_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 20 and d = 10, thus

`A_(n)` = 10 + 10(n - 1) = 10 + 10n - 10 = 10n + 10