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What is the equation for the nth term of the arithmetic sequence where a1 = 32 and d = –7?

an=32+7n
an=32-7n
an=28-7(n-1)
an=32+7(n-1)

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akposevictor

Given that the first term and the common difference of an arithmetic sequence are -7 and 32 respectively, the equation for the nth term is: [tex]\mathbf{a_n = 32 -7(n - 1)}[/tex]

Recall:

  • nth term of arithmetic sequence is expressed as: [tex]a_n = a + (n - 1)d[/tex]
  • Where, a is the first term, d is the common difference.

  • Given the following for an arithmetic sequence:

d = -7

[tex]a_1 = 32[/tex]

Substitute the values into [tex]a_n = a + (n - 1)d[/tex]

  • Thus:

[tex]a_n = 32 + (n - 1)-7\\\\\mathbf{a_n = 32 -7(n - 1)}[/tex]

Therefore, given that the first term and the common difference of an arithmetic sequence are -7 and 32 respectively, the equation for the nth term is: [tex]\mathbf{a_n = 32 -7(n - 1)}[/tex]

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