Question

Find the 7th term of the arithmetic sequence. -3x+6, -7x-1, -11x-8

Answer 1

`\({a}_(7) = - 27 x - 36\)`

Explanation:

Write the general term through the pattern:
`a_(n) =(x+13)+n(-4x-7)`

Substitute and calculate:
`\({a}_(7) = - 27 x - 36\)`

Answer 2

We can find the common difference of the arithmetic sequence by subtracting any two consecutive terms. Let's subtract the second term from the first:

(-7x-1) - (-3x+6) = -7x - 1 + 3x - 6 = -4x - 7

So the common difference is -4x - 7.

To find the seventh term of the arithmetic sequence, we can start with the first term and add the common difference six times, since we want the seventh term. Thus, the seventh term is:

-3x + 6 + 6(-4x - 7)

Simplifying the expression, we get:

-3x + 6 - 24x - 42

-27x - 36

Therefore, the seventh term of the arithmetic sequence is -27x - 36.