Equations of Geometric Sequences Quiz

Answer explanation

The general formula for the nth term of a geometric sequence is given by \( a_n = a \cdot r^{n-1} \). This formula reflects that each term is the first term multiplied by the common ratio raised to the power of (n-1).

Tags

CCSS.HSF.BF.A.2

Answer explanation

The first term is 2 and the common ratio is 3 (6/2 = 3). The nth term of a geometric sequence is given by \( a_n = a_1 \cdot r^{n-1} \). Thus, \( a_n = 2 \cdot 3^{n-1} \) is correct.

Tags

CCSS.HSF.BF.A.2

Answer explanation

In a geometric sequence, the nth term is given by \( a_n = a_1 \cdot r^{n-1} \). Here, \( a_1 = 5 \) and \( r = -2 \), so the equation is \( a_n = 5 \cdot (-2)^{n-1} \), which matches the first answer choice.

Tags

CCSS.HSF.BF.A.2

Answer explanation

The sequence is a geometric progression where each term is half of the previous one. The nth term can be expressed as \( a_n = 8 \cdot \left(\frac{1}{2}\right)^{n-1} \), matching the correct choice.

Tags

CCSS.HSF.BF.A.2

Answer explanation

In a geometric sequence, the common ratio r is found by dividing any term by the previous term. Here, r = 21/7 = 3. Thus, the common ratio is 3, making the correct answer choice 3.

Tags

CCSS.HSF.BF.A.2

Answer explanation

The nth term of a geometric sequence is given by the formula a_n = a_1 * r^(n-1). Here, a_1 = 10 and r = 0.5, so the equation becomes a_n = 10 * 0.5^(n-1), which matches the correct choice.

Tags

CCSS.HSF.BF.A.2

Answer explanation

The common ratio r is found by dividing a_2 by a_1. Here, r = a_2 / a_1 = 6 / 12 = 0.5. Thus, the correct answer is 0.5.

Tags

CCSS.HSF.BF.A.2

Answer explanation

The sequence alternates signs and doubles in absolute value. The formula for the nth term is given by a_n = -3 * (-2)^(n-1), which captures both the sign change and the doubling pattern.

Tags

CCSS.HSF.BF.A.2

Answer explanation

In a geometric sequence, the nth term is given by \( a_n = a_1 \cdot r^{n-1} \). Here, \( a_1 = 1 \) and \( r = 4 \), so \( a_n = 1 \cdot 4^{n-1} \). Thus, the correct choice is \( a_n = 1 \cdot 4^{n-1} \).

Tags

CCSS.HSF.BF.A.2

Answer explanation

The first term of the geometric sequence is found by evaluating the formula at n=1. Substituting n=1 into a_n = 9 \cdot 5^{n-1} gives a_1 = 9 \cdot 5^{0} = 9. Thus, the first term is 9.

Tags

CCSS.HSF.BF.A.2