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]
[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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