Question

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 - a58 = 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

$-3,4,11,18$

As you can observe, this sequence as a difference of 7, that is, each new term is the sum of the previous term with seven.

Arithmetic sequences are defined by

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

Where, in this case, we have

$\begin{gathered} a_1=-3 \\ d=7 \\ n=58 \end{gathered}$

Replacing these values, we have

$a_{58}=-3+(58-1)7=-3+(57)7=-3+399=396$

The 58th term is 396.

(a) The reason why Amanda is wrong is she used 18 as the first term which is not correct because 18 is the fourth term of the sequence.

(b) To correct her mistake, she just needs to use -3 as the first term in the formula.