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20-10-2020
Mathematics

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The first term in an arithmetic sequence is 5. The third term in the sequence is -1. The tenth term in the sequence is -22.

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21-10-2020

Answer:

[tex]\bold {a_n=-3n+8}[/tex]

Step-by-step explanation:

[tex]a_n=a_1+d(n-1)\\\\a_3=5+d(3-1)\\\\-1=5+2d\\\\-6=2d\\\\d=-\frac62=-3\\\\\\a_n=5+(-3)(n-1)\\\\a_n=5-3n+3\\\\a_n=-3n+8[/tex]

Check: [tex]a_{10}=-3(10)+8=-30+8=-22[/tex]

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