Geometric Sequences Trivia Questions Quiz

Explanation
The sequence -3, -6, -12, -24, ... is geometric because each term is obtained by multiplying the previous term by a constant factor of -2.

Explanation
The given sequence is a geometric sequence with a first term of 3 and a common ratio of -4. To find the fifth term, we can use the formula for the nth term of a geometric sequence: an = a1 * r^(n-1). Plugging in the values, we get a5 = 3 * (-4)^(5-1) = 3 * (-4)^4 = 3 * 256 = 768. Therefore, the fifth term in the sequence is 768.

Explanation
The given sequence is a geometric sequence where each term is obtained by multiplying the previous term by a constant factor. In this case, the common ratio is -4. To find the 7th term, we can use the formula for the nth term of a geometric sequence: an = a1 * r^(n-1). Plugging in the values, we get a7 = -48 * (-4)^(7-1) = -48 * (-4)^6 = -48 * 4096 = -196,608. However, this answer does not match any of the given options. Therefore, the correct answer is not available or there may be an error in the question.

Explanation
In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio. To find the 15th term, we start with the first term and multiply it by the common ratio 14 times. Given that the 15th term is 32,768, it means that the first term multiplied by the common ratio 14 times equals 32,768. The only choice that satisfies this condition is 2 as the first term and 2 as the common ratio.

Explanation
The given geometric sequence is obtained by multiplying each term by 0.8. To find the next term, we multiply the last term (32) by 0.8, resulting in 25.6. To find the term after that, we again multiply by 0.8, giving us 20.48. Therefore, the next two terms of the geometric sequence are 25.6 and 20.48.