Katie recently retired and met with her financial planner. She arranged to recieve 57000 the first year. Because of inflation, each year she will get 820, ore than she recieved the previous year. What income will she recieve in her tenth year of retirement?

Question

Mathematics

Red Velvet

26 September, 02:58

Katie recently retired and met with her financial planner. She arranged to recieve 57000 the first year. Because of inflation, each year she will get 820, ore than she recieved the previous year. What income will she recieve in her tenth year of retirement?

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Answers (1)

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Molly · Answer 1

Answer: she will receive 64380 in her tenth year

Step-by-step explanation:

She arranged to receive 57000 the first year. Because of inflation, each year she will get 820 more than she received the previous year. This means that she is getting an additional 820 each year. This increase is in arithmetic progression. The formula for the nth term of an arithmetic progression is expressed as

Tn = a + (n - 1) d

Where

Tn is the value of the nth term of the sequence

a is the first term of the sequence

d is the common difference

n is the number of terms in the sequence

From the information given

a = 57000 because it is her first income

n = 10

d = 820

Tn is the income that she will receive in her tenth year of retirement. Therefore,

Tn = 57000 + (10-1) * 820

Tn = 57000 + 7380

Tn = 64380