Question

The terms shown below are the first 3 terms of a geometric sequence whose common ratio is negative. 17,3x-57,153. (a) Determine the value of the common ratio for this sequence. Show how you found your answer. (b) Determine the value of x algebraically.

Answer 1

The common ratio of the geometric sequence 17, 3x-57, 153, which has a negative ratio, is found to be -3 after algebraic calculations. The value of x is determined to be 6.5.

Step-by-step explanation:

The question involves finding the common ratio and then the value of x in a geometric sequence.

For the given geometric sequence 17, 3x-57, 153, we find the common ratio by dividing the second term by the first term, which gives us:

(3x - 57) / 17 = r, where r is the common ratio.

For a geometric sequence with a negative common ratio, we take the third term and divide it by the second term, giving us:

153 / (3x - 57) = -r

From this, we can solve for x using the equality (-r) * (r) = 1, and then solve the resulting expression algebraically to find x.

The value of x comes out to be 6.5 after algebraic simplification.

Therefore, the common ratio is -3.