Question

1 2 3 2 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) 058 USE COMPLETE SENTENCES/ESCRIBE EN ORACIONES COMPLETAS a. What is her mistake? b. How should she correct it?

Answer 1

we have the sequence

-3,4,11,18,...

a1=-3

a2=4

a3=11

a4=18

Find the common difference d

d=a2-a1=4-(-3)=7

d=a3-a2=11-4=7

d=a4-a3=18-11=7

so

d=7

This is an aritmetic sequence

The explicit formula is equal to

an=a1+d(n-1)

substitute the given values

an=-3+7(n-1)

Find the 58th term

we have

n=58

substitute

an=-3+7(58-1)

amanda's mistake

she used 18 instead of -3 as firts term in the formula