Question

Given the functions f(n) = 11 and g(n) = -2(n - 1), combine them to create an arithmetic sequence, an, and solve for the 31st term.


   an = 11 - 2(n - 1); a31 = -49
   an = 11 - 2(n - 1); a31 = -51
   an = 11 + 2(n - 1); a31 = 71
   an = 11 + 2(n - 1); a31 = 73

Answer 1

an = 11 - 2(n - 1); a31 = -49

Answer 2

Option A is correct

`a_n = 11-2(n-1)` and
`a_(31) = -49`

Explanation:

Given the functions:

`f(n) = 11`

`g(n) = -2(n-1)`

then;

combine them to create an arithmetic sequence i.e,

`a_n = f(n)+g(n)`

⇒
`a_n = 11-2(n-1)` where n is the number of terms

To find the 31st term.

Substitute n =31 we have;

`a_n = 11-2(31-1)`

⇒
`a_(31)=11-60 = -49`

Therefore, we have an arithmetic sequence,

`a_n = 11-2(n-1)` and
`a_(31) = -49`