Question

A tree is currently 10 feet tall and grows 2 feet per year. Write an arithmetic sequence in explicit formula that can model this scenario.

Answer 1

Given:

A tree is currently 10 feet tall and grows 2 feet per year.

To find:

The arithmetic sequence in explicit formula that can model this scenario.

Solution:

Current height of tree is 10 feet. So, initial value of the arithmetic sequence is a=10.

It grows 2 feet per year. So, common difference is d=2.

The explicit formula for an arithmetic sequence is

`f(n)=a+(n-1)d`

where, a is first term and d is common difference.

Put a=10 and d=2 in the above formula.

`f(n)=10+(n-1)2`

`f(n)=10+2n-2`

`f(n)=8+2n`

Therefore, the explicit formula for given scenario is
`f(n)=8+2n`.