Question

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 18+7(58 - 1) аѕ8 USE COMPLETE SENTENCES/ESCRIBE EN ORACIONES COMPLETAS a. What is her mistake? b. How should she correct it?

Answer 1

1) Analyzing the sequence, this is an Arithmetic Sequence.

-3,4,11,18

a)

We have a common ratio for that Arithmetic Sequence of r =7

The explict formula for that, Arithmetic Sequence is:

a_n=a_1 +(n-1)r

an=-3 +(n-1)7

So for the 58th term, the explicit formula would be:

a_58 =-3 +(57)7

a_58=-3+399

a_58=396

b) Amanda has failed because she has chosen the last term of the sequence (58 instead of -3). Unlike the general explicit formula. To correct her work, just replace 58 by -3.