Question

7. Which Statement is TRUE? a. 1,-5, 25, -125, ... is a geometric sequence because to get to the next term, you multiply -5 times the previous term. b. 1, 8, 15, 22, 29, ... is a geometric sequence because to get to the next term, you multiply 8 times the previous term. C. 1,-4, -9,-14, ... is a geometric sequence because to get to the next term, you add - 5 to the previous term. d. 1, 1.5, 2, 2.5, is a geometric sequence because to get to the next term, you add 0.5 to the previous term. I.

Answer 1

the answer is option A

the series is given as 1, -5, 25, -125....

now to test if this is a geometric sequence, let's find the common ratio between two successive numbers

take the fourth term and divide it by the third term

$-\frac{125}{25}=-5$

take the third term and divide it by the second term

$\frac{25}{-5}=-5$

take the second term and divide it by the first term

$-\frac{5}{1}=-5$

from the observation above, they all have a common ratio of -5 and that implies to find the next term, simply multiply the term -5 to the prevoius term