Question

Given the arithmetic sequence 2, 8, 14, 20, ...
Write the explicit rule and find a30

Answer 1

see explanation

Explanation:

The n th term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 2 and d = 8 - 2 = 6, thus

`a_(n)` = 2 + 6(n - 1) = 2 + 6n - 6 = 6n - 4

Hence

`a_(30)` = (6 × 30) - 4 = 180 - 4 = 176