Question

In a sequence of numbers, a, = 16, a. = 21, a. = 31 and a, = 36, based on this information, Which of the following equation that can be used to find the nth term in the sequence, an?
an = 3n + 2
an = 5n + 1
an = 2n + 2
an = 5n + 3

Answer 1

Answer:

            The second:  aₙ = 5n + 1

Step-by-step explanation:

We are checking the sequences by calculating given terms from equations:

$a_n = 3n + 2\\\\a_3 = 3\cdot3 + 2=11\ne16\ \implies\ not\ this\ equation\\\\\\a_n = 5n +1\\\\a_3 = 5\cdot3 +1=16\\\\a_4 = 5\cdot4 +1=21\\\\a_6 = 5\cdot6 +1=31\\\\a_7 = 5\cdot7 +1=36\\\\\ so\ this\ is\ the\ equation\\\\\\Just\ to\ be\ sure:\\a_n = 2n + 2\\a_3 = 2\cdot3 + 2=8\ne16\ \implies\ not\ this\ equation\\\\a_n = 5n + 3\\a_3 =5\cdot3 + 3=18\ne16\ \implies\ not\ this\ equation$