Question

3 1 6 . 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?

Answer 1

The given sequence is

`-3,4,11,18\ldots`

Amanda was asked to find the 58th term.

Amanda's Explicit Formula is

`a_(58)=18+7\mleft(58-1\mright)`

The standard explicit formula for an arithmetic sequence is given by

`a_n=a_1+d(n-1)`

Where aₙ is the nth term, a₁ is the first term and d is the common difference

The common difference is basically the difference between any two consecutive terms

d = 18 - 11 = 7

d = 11 - 4 = 7

d = 4 - (-3) = 4 + 3 = 7

So the common difference is 7.

The first term in the sequence is -3

So the correct explicit formula for the 58th term becomes

`a_(58)=-3+7(58-1)`

Comparing it with Amanda's explicit formula we see that she made mistake with regard to the first term.

She wrote 18 instead of -3

Therefore, Amanda needs to replace 18 with -3 to correct the mistake.