Answered

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If the 6th term of an arithmetic sequence is
12 and the 15th term is -15, find the first
term and the common difference.

Sagot :

Answer:

d = -3    

[tex]a_{1}[/tex] = 27

Step-by-step explanation:

You have to use the formula [tex]a_{n} = a_{1} + (n - 1)d[/tex] two times, once for the 6th term and once for the 15th term

(1)    [tex]12 = a_{1} + (6 - 1)d[/tex]          (2)    [tex]-15 = a_{1} + (15 - 1)d[/tex]

        [tex]12 = a_{1} + 5d[/tex]                         [tex]-15 = a_{1} + 14d[/tex]  Change signs and add to (1)

        [tex]15 = - a_{1} - 14d[/tex]

         27 = -9d

          d = -3                                  - 15 = [tex]a_{1}[/tex] + 14(-3)

                                                      - 15 = [tex]a_{1}[/tex] - 42

                                                          [tex]a_{1}[/tex] = 27

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