Finding the Nth Term of a Geometric Sequence

If a₄ = 81 and r = - 3/2, what is the first term of the geometric sequence (a₁) ?

• 3

• 24

• - 3

• - 24

Answer explanation

In a geometric sequence, a_n = a_1 * r^(n-1). Given a_4 = 81 and r = -3/2, we find a_1: 81 = a_1 * (-3/2)^(3). Solving gives a_1 = -24. Thus, the first term is -24.

What is the first term of the geometric sequence (a₁) if a₄ = - 2 and a₇ = 16?

• 1/4

• 1/2

• - 1/4

• - 1/2

Answer explanation

In a geometric sequence, a_n = a_1 * r^(n-1). Given a_4 = -2 and a_7 = 16, we can set up the equations: a_1 * r^3 = -2 and a_1 * r^6 = 16. Dividing these gives r^3 = -8, so r = -2. Substituting r back, a_1 = 1/4.

If a₁₄ = - 5 and r = - 1, what is the first term of the geometric sequence (a₁) ?

• 5

• 1

• - 5

• - 1

Answer explanation

In a geometric sequence, the nth term is given by a_n = a_1 * r^(n-1). Here, a_14 = -5 and r = -1. Thus, -5 = a_1 * (-1)^(14-1) = a_1 * (-1). Solving gives a_1 = 5.

What is the next term in the geometric sequence 4 , -16 , 64 , ____?

• -128

• -192

• -256

• -266

5. Find the  5th term of a geometric sequence 4 , -8 , 16, ...?

• A.  128

• B. 124

• C. 108

• D. 64

Find the 9th term of the geometric sequence :

• A.   768

• B.   786

• C.  796

• D.  1536

Find the 9th term of the geometric sequence in which the third term is 32 and the common ratio is 4.

•    32 768

•    131 072

•   524  288

•   2 097 152

What is the 6th term of the geometric sequence \frac{2}{16}\,\frac{2}{4\ },\ 2\ ,\ 8\ ,\ ...\

• A. 32

• B. 128

• C. 512

• D. 2048

Find the seventh term of a geometric sequence where the third is 18 and the common ratio is 3.

• A.  162

• B. 486

• C. 1458

• D. 4374

Find the common ratio for the geometric sequence that has first term is 3 and fifth term is 48.

• 1

• 2

• 3 

• 4