Question

1.2,3,7.5,18.75, which formula can be used to describe the sequence

Answer 1

Answer:

$a_{n}=1.2 \times(2.5)^{n-1}$

Step-by-step explanation:

If we observe the given sequence, we find that the ratio of two consecutive terms is the same. i.e.

$\frac{3}{1.2}=2.5\\\\\frac{7.5}{3}=2.5\\\\ \frac{18.75}{7.5}=2.5$

Such a sequence in which the ratio of consecutive terms remain the same is know as Geometric Sequence. Following formula is used to represent a Geometric Sequence:

$a_{n}=a_{1}\times(r)^{n-1}$

Here:

$a_{n}$ is the general term. Using the value of n =1,2,3 ... will give us the term of the sequence.

$a_{1}$ is the first term which is 1.2 in this case.

r represents the common ratio which is 2.5.

Using these values we get:

$a_{n}=1.2 \times(2.5)^{n-1}$

This formula can be used to represent the given sequence.