Which of the following?

Question

The second and third terms of a geometric sequence are 2.5 and 1.25, respectively. Which of the following is the first term? 

 

a) -5

b) -2.5

c) 0.625

d) 3.75

e) 5

 

Please show all your work. 

Answer 1

The answer is E

 

Explanation:  In geometric series, the ratio of each term to its preceding term is a constant.

 

let's write the sequence as:    a0, a1, a2, ....., an

 

The ratio of a4/ a3 = a3/a2 = a2/a1 = a1/a0 = r    In general:  an/a(n-1) = r

 

So let's divide the third term by the second term:  1.25/ 2.5 = 0.5

 

There fore 2.5/a1 = 0.5.   You solve this for a1 and get a1 = 5

 

hope that helps