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3. (2 points) Given the sequence - 3, 4, 11, 18, ... Amanda was asked to find the 58th term. She wrote the explicit formula below. Her teacher Ms. Felton informs her that her response is incorrect. Explain where she made a mistake. Then correct her mistake. Amanda's Explicit Formula 058 18+7(58 - 1) USE COMPLETE SENTENCES/ESCRIBE EN ORACIONES COMPLETAS a. What is her mistake? b. How should she correct it?

User Zack ISSOIR
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1 Answer

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Arithmetic Sequences

They are lists of numbers with a predictable pattern: Each term is obtained as the previous one plus a constant number, called common difference.

The sequence given in the question is: -3, 4, 11, 18,...

The common difference can be obtained subtracting two consecutive terms, for example:

r = 4 - (-3) = 7

We can also get the same number subtracting the 3rd term with the 2nd term:

r = 11 - 4 = 7

Every time we do that, we get the very same number, thus we know the common difference is r = 7.

Another important parameter is the first term, in our case it is

a1 = -3

The number besides the 'a' means the counter of terms, thus the second term is called a2 and can be computed as:

a2 = a1 + r = -3 + 7 = 4

The third term is calculated by:

a3 = a2 + r = 4 + 7 = 11

But it also can be obtained by

a3 = a1 + 2*7 = -3 + 14 = 11

Inferring the general formula for an arithmetic sequence we get

an = a1 + (n-1)*r

a)

If we wanted to calculate the term 58, the formula will become:

a58 = -3 + 7 * (58-1)

Since Amanda used the formula

a58 = 18 + 7 * (58-1)

Her mistake was the incorrect value of a1.

b)

The correct value is

a58 = -3 + 7 * 57 = -3 + 399 = 396

a58 = 396

User Mezbah
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