Tom has taken out a loan for college. He started paying off the loan with a first payment of $200. Each month he pays, he wants to pay back 1.2 times as the amount he paid the month before. Explain to Tom how to represent his first 30 payments in sigma notation. Then explain how to find the sum of his first 30 payments, using complete sentences. Explain why this series is convergent or divergent.
Tom has taken out a loan for college. He started paying off the loan with a first payment of $200. Each month he pays, he wants to pay back 1.2 times as the amount he paid the month before. Explain to Tom how to represent his first 30 payments in sigma notation. Then explain how to find the sum of his first 30 payments, using complete sentences. Explain why this series is convergent or divergent.
From given data the first payment of Tom = $200
The second payment is 1.2 times of first payment, hence the second payment = $200(1.2)
The third payment is 1.2 times of second payment, hence the third payment = $200(1.2)2
The fourth payment is 1.2 times of third payment, hence the fourth payment = $200(1.2)3
continue on this way ............
The 30th payment is 1.2 times of 29th payment, hence the 30th payment = $200(1.2)29
Tom first 30 payments in sigma notation. = 200 + 200(1.2) +200(1.2)2+200(1.2)3+.......+200(1.2)29
= 200(1.2)0 + 200(1.2)1 +200(1.2)2+200(1.2)3+.......+200(1.2)29
=
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