Question

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.

Answer 1

`\bold {a_n=-3n+8}`

Explanation:

`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`

Check:
`a_(10)=-3(10)+8=-30+8=-22`