John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times as the amount he paid the month before. Explain to John how to represent his first 20 payments in sigma notation. Then explain how to find the sum of his first 20 payments, using complete sentences. Explain why this series is convergent or divergent.

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Mathematics

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20 August, 02:21

John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times as the amount he paid the month before. Explain to John how to represent his first 20 payments in sigma notation. Then explain how to find the sum of his first 20 payments, using complete sentences. Explain why this series is convergent or divergent.

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Morgan Holloway · Answer 1

Ok let me explain it like this: If each payment is 100 * (1.1^ (n-1)) Then what you need to u se is the sigma sign with n=1 below and 20 above.

So that will be $5727.50

After this we can say that t his is divergent since each terms is larger. Hope this works for you