Question

Sarah has saved $150. She wants to double the amount she saves each month. As an incentive, Sarah’s grandma says if she saves that amount, she will give her an additional $50 each month. What are the recursive formula and first term for Sarah’s saving’s?

Answer 1

A₁ = $150.

Explanation:

We know that:

Sarah has saved $150 at the moment.

She wants to double the amount that she saves each month, so the next month she needs to save 2*$150 = $300

And if she saves the $300, then her grandma will give her another $50.

Then, if the previous month Sarah saved A, then the next month she will get the double of A plus $50, which is:

2*A + $50

Then the recursive relation is just:

Where Aₙ is the amount that she saves in the n-th month, and the first term of the sequence is the initial amount that she saved, so we have:

A₁ = $150.