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Given the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem. An=-11+7b. Find a34



Answer :

crisforp
A1 = -11 + 7 = - 4;
A2 = - 11 + 14 = 3 ;
A3 = - 11 + 21 = 10 ;
A4 = - 11 + 28 = 17 ;
A5 = - 11 + 35 = 24 ;
A34 = - 11 + 7 × 34 = - 11 + 238 = 227 ;

In the arithmetic sequence:

  • The first five terms are: {-11, -4, 3, 10, 17}.
  • a34 = 227.

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  • In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d, and the general equation for the nth term is:

[tex]a_n = a_0 + nd[/tex]

  • In which [tex]a_0[/tex] is the first term.

In this question, the sequence is defined by:

[tex]A_n = -11 + 7n[/tex]

  • The first term is: -11.
  • Then:

[tex]A_1 = -11 + 7 = -4[/tex]

[tex]A_2 = -11 + 14 = 3[/tex]

[tex]A_3 = -11 + 21 = 10[/tex]

[tex]A_4 = -11 + 28 = 17[/tex]

The first five terms are: {-11, -4, 3, 10, 17}.

For a34:

[tex]A_{34} = -11 + 7(34) = 227[/tex]

A similar problem is given at https://brainly.com/question/23842987

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