Question

Which formula can be used to describe the sequence? 1.2, 3, 7.5, 18, 7.5, ...

Answer 1

The given sequence is 1.2, 3, 7.5, 18.75, ...,
This is a geometric sequence with common ratio of 2.5, because
3/1.2 = 2.5
7.5/3 = 2.5
18.75/7.5 = 2.5

The 1st term is   a₁ = 1.2(2.5)⁰
The 2nd term is a₂ = 1.2(2.5)¹
The 3rd term is  a₃ = 1.2(2.5)²
and so on

Therefore the sequence obeys the formula
f(x) = 1.2(2.5)ˣ⁻¹

Answer: $f(x) = 1.2(2.5)^{x-1}$

Answer 2

Answer:

Option A) $1.2(2.5)^{x-1}$

Step-by-step explanation:

We are given a series:

$1.2, 3, 7.5, 18.75, ...$

We know that the given series is a geometric series as

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

Geometric Series:

• A geometric series is a series with a constant ratio between successive terms.
• The first term is represented by a
• In the given series a = 1.2
• The common ratio is denoted by r
• For the given series r = 2.5

The $n^{th}$ term of a geometric series is given by:

$a_n = a(r)^{n-1}$

$a_1= 1.2\\a_2 = 1.2(2.5)^{2-1} = 3\\a_3 = 1.2(2.5)^{3-1} = 7.5\\a_4 = 1.2(2.5)^{4-1} = 18.75$

Thus, the general term of the given series can be formulated with the help of $f(x) = 1.2(2.5)^{x-1}$

Option A) $1.2(2.5)^{x-1}$