1st term in sequence is 6-4th term is -6, the 8th term is -22 write a function that can be used to find the nth term of the sequence

EXPLANATION

The nth term of the sequence is given by

Where

is the first term and

is the constant difference.

We were given that,

S we just need the common difference to write the nth term.

We can get that from another information given to us.

We were also given that the 4th term is 6. This gives the equation.

We substitute

to obtain

Or

This implies,

We substitute these values into the general formula to obtain,

This gives us,

Hence the nth term of the sequence is,

= 10 - 4n

this is an arithmetic sequence with n th term

= + (n - 1 )d

where is the first term and d the common difference

given = - 6, then

6 + 3d = - 6 ( subtract 6 from both sides )

3d = - 12 ( divide both sides by 3 )

d = - 4 ← common difference hence

= 6 - 4 (n - 1 ) = 6 - 4n + 4 = 10 - 4n