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An Ontario lottery has the following structure, the first person drawn from the names wins $15 000. Each subsequent person drawn wins $150 less than the person before. The last person drawn wins $6000.
a) Write the first four terms of the sequence that represents the winnings.
b) Determine a and d for the sequence.
c) Determine an explicit formula for the general term.

Respuesta :

fichoh
  • The first four terms are : 15000, 14850, 14700, 14550
  • a = 15000 ; d = -150
  • The explicit formula is : [tex] a_{n} = - 150n \: + 15150[/tex]

The first term of the sequence, a = 15,000

Each subsequent winner gets $150 less

Hence, the common difference, d = - $150

The first four terms :

First term, a1 = $15000

Second term, a2 = a - d = $15000 - $150 = $14850

Third term, a3 = a2 - d = $14850 - $150 = $14700

Fourth term, a4 = a3 - d = $14700 - $150 = $14550

a, for the sequence is the first term = $15000

d, for the sequence is the common $150 (difference between successive wins).

Explicit formula for the general term :

[tex] a_{n} \: = nd \: + c [/tex]

For n = 1

[tex] 15000 = 1( - 150) + c[/tex]

[tex]15000 = - 150 + c[/tex]

[tex]c = 15150[/tex]

Hence, the explicit formula for the nth term is :

[tex] a_{n} \: = - 150n \: + 15150[/tex]

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