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Unit 3 - Task 3 - (10 points)
Your job is as an administrative assistant for factory operations for a company producing
Whatchamacallits. Your boss hands you the production information for the factory's
production of Whatchamacallits: 3 Whatchas in the first hour, 7 total after hour 2, 11
total after 3 hours and 15 after 4 hours. You are tasked to produce an equation that
models the number of Whatchas produced given the hours worked, and to find the
predicted number of Whatchas produced if the factory can run for 50 hour
uninterrupted.
Find an explicit formula that models the production for the nth term of the sequence
and use the equation to find the 50th term in the sequence. Show your reasoning for
the equation.

Sagot :

Abidemiokinidn

The 50th term in the sequence is 199

Arithmetic sequence

The nth term of an arithmetic sequence is expressed as:

Tn = a+ (n - 1)d

where:

  • a is the first term
  • n is the number of terms
  • d is the common difference

The sequence formed by the amount of Whatchamacallits produced as;

3, 7, 11, 15...

a = 3

d = 11-7 = 7-3 = 4

Substitute

Tn = 3 + (n-1) * 4
Tn = 3 + 4n -4

Tn = 4n - 1

Hence the explicit formula that models the production for the nth term of the sequence is Tn = 4n - 1

If n = 50

T50 = 4(50) - 1

T50 = 199

Hence the 50th term in the sequence is 199

Learn more on sequence here; https://brainly.com/question/6561461

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