Question

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 13 , 17 , 21 , . . . 13,17,21,... Find the 43rd term. Find the 43rd term.

Answer 1

a₄₃ = 181

Explanation:

there is a common difference between consecutive terms, that is

17 - 13 = 21 - 17 = 4

this indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 13 and d = 4 , then

a₄₃ = 13 + (42 × 4) = 13 + 168 = 181