Question

A certain species of tree grows an average of 3.8 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall

Answer 1

f(n)=500+3.8n

Answer 2

Thanks!

Answer 3

can you show me how you got that?

Answer 4

5 meters=500 cm, every week + 3.8 cm => f(n)

Answer 5

Thank you! if you don't mind, could you help me with a few more?

Answer 6

Sure

Answer 7

Use mathematical induction to prove the statement is true for all positive integers n.

The integer n3 + 2n is divisible by 3 for every positive integer n

Answer 8

( n + 1 )^3 + 2( n + 1 ) = ( n^3 + 3n^2 + 3n + 1 ) + ( 2n + 2 )
= ( n^3 + 2n ) + ( 3n^2 + 3n + 3 )
= ( n^3 + 2n ) + 3( n^2 + n + 1 )
Therefore ( n^3 + 2n ) is divisible by 3