Question

one term of an arithmetic sequence is a17=82 and d=-6. write a rule for the nth term of the sequence. then find a10

Answer 1

`a_(10)=124`

Explanation:

In an arithmetic sequence, we are given that:

`a_(17)=82\\d=-6`

The nth term of an arithmetic sequence,
`a_n=a+(n-1)d`

When n=17,
`a_(17)=82,d=-6`, we have:

`a_(17)=a+(17-1)(-6)`

82=a+(16)(-6)

82=a-96

a=82+96

a=178

Therefore, the 10th term of the sequence

`a_(10)=178+(10-1)(-6)\\=178+9(-6)\\=178-54\\a_(10)=124`