Question

Write the explicit equation for the sequence 5,8,11,14

Answer 1

Consecutive terms differ by 3, so


`a_n=a_(n-1)+3=a_(n-2)+2*3=a_(n-3)+3*3=\cdots=a_1+(n-1)*3`

Since the first term is
`a_1=5`, the formula for the sequence is


`a_n=5+3(n-1)=3n+2`