Geometric Finding Nth Term

• common difference

• nth term

• common ratio

• first term

Solving for the nth term of geometric sequence, given that a₁ = 4 and r= 6, what is the value of the 4th term?

• 144

• 864

• 124

• 764

Answer explanation

To find the 4th term of a geometric sequence, use the formula a_n = a_1 * r^(n-1). Here, a_1 = 4, r = 6, and n = 4. Thus, a_4 = 4 * 6^(4-1) = 4 * 216 = 864. Therefore, the 4th term is 864.

Find the 10th term of the following geometric sequence

5, 20, 80, 320, ...

• 81,920

• 327,680

• 1,310,720

• 5,242,880

Answer explanation

The sequence is geometric with a common ratio of 4. The nth term is given by a_n = a_1 * r^(n-1). Here, a_1 = 5, r = 4, and n = 10. Thus, a_{10} = 5 * 4^9 = 1,310,720, which is the correct answer.

To find the next term in a geometric sequence …

• add the common difference d

• multiply by the common ratio r

• subtract the common difference d

• divide by the common ratio r

Answer explanation

In a geometric sequence, each term is found by multiplying the previous term by the common ratio r. Therefore, to find the next term, you multiply by the common ratio r.

Please click on the picture and read carefully

• a

• b

• c

• d

In the sequence of numbers, g₃ = -27, g₄ = -81, g₅ = -243, g₆ = -729, and g₇ = -2187. Based on this information, which equation can be used to find the nth term in the sequence, g_n?

• g_n = -27 ∙ 3ⁿ⁺¹

• g_n = -27 ∙ 3^n-1

• g_n = -3 ∙ 3ⁿ⁺¹

• g_n = -3 ∙ 3^n-1

What is the 11th term of the geometric sequence?

• -5120

• 97,656,250

• 19,531,250

• -19,531,250

Values of the terms of a geometric sequence are graphed in the figure above.  Which of the following is an expression for the nth term of the geometric sequence?

Find the 11^th term for:  64, -32, 16, -8, …  

• -.0625

• .0625

• -.03125

• .03125