Answer: C: 2.5, 12.5, 62.5, 312.5
Step-by-step explanation:
Let us remember that in a geometric sequence:
ratio = [tex]\frac{a_{2} }{a_{1}}[/tex]
We know that [tex]a_{1}[/tex] (first term) is 2.5. So plug in the numbers into the above formula:
5 = [tex]\frac{a_{2} }{2.5}[/tex]
Multiply both sides by 2.5 to solve for [tex]a_{2}[/tex] (second term):
5 × 2.5 = 12.5
By process of elimination, it is obvious the correct answer is C.
We can double check your answer by checking the rate is 5 by dividing:
For example, 62.5 ([tex]a_{3}[/tex]) divided by 12.5 ([tex]a_{2}[/tex]) is appropriately 5.
Similarly, 312.5 ([tex]a_{4}[/tex]) divided by 32.5 ([tex]a_{3}[/tex]) is again 5, confirming our answer to be correct.
