Write the first five terms of the geometric sequence with a =

Question

Write the first five terms of the geometric sequence with a = - 2 and a fourth term of -54.
A) -2, -3, -21, -51, -165
B) -2, -6, -18, -54, -162
C) -2, -5, -8, -11, -14
D) -2, 3, -16, 51, -162

Quizplus · Accepted Answer

To find the common ratio, we divide the fourth term by the first term raised to the power of three (since the fourth term is the third power of the first term multiplied by the common ratio): 
-54 / (-2)^3 = -54 / -8 = 6.75
Therefore, the common ratio is 6.75. 
Using this common ratio, we can find the second term: 
-2 x 6.75 = -13.5
Then, we can find the third term: 
-13.5 x 6.75 = -91.125
And the fourth term is given as -54. 
Finally, we can find the fifth term: 
-91.125 x 6.75 = -615.09375
Therefore, the first five terms of the sequence are: 
-2, -13.5, -91.125, -54, -615.09375
which matches Choice B.