Question

Find the 11th term of the arithmetic sequence x+9, -3x + 5−3x+5, -7x+1, ...

Answer 1

`-39x-31`

Explanation:

`\text{First term,}~ a = x+9\\\\\text{Common difference,}~ d = -3x+5 -x -9 = -4x-4\\\\\text{nth term,}~ a_n = a + (n-1) d\\\\~~~~~~~~~~~~~~~~~~=x+9+(n-1)(-4x-4)\\\\~~~~~~~~~~~~~~~~~~=x+9-4nx+4x-4n+4\\\\~~~~~~~~~~~~~~~~~~=5x-4nx-4n+13\\\\\text{11th term}~ a_(11) = 5x-4(11)x -4(11) + 13\\\\~~~~~~~~~~~~~~~~~~~=5x-44x-44+13\\\\~~~~~~~~~~~~~~~~~~~=-39x-31`