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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?

Sarah has saved 150 She wants to double the amount she saves each month As an incentive Sarahs grandma says if she saves that amount she will give her an additi class=

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Answer:

A₁ = $150.

Step-by-step 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.

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