Question

What the explicit formula of 3 5 7 9

Answer 1

Answer:

$a_{n}=3+2(n-1)$

Step-by-step explanation:

Given:

The given sequence is 3, 5, 7, 9

The difference between the second and first term is 5 - 3 = 2

The difference between the third and second term is 7 - 5 = 2

The difference between the fourth and third term is 9 - 7 = 2

So, there is a common difference of 2. Thus a sequence which has the same difference is known as an arithmetic sequence.

The explicit formula to determine the $n^{th}$ term of an arithmetic sequence is given as:

$a_n=a_1+(n-1)d$

Where, $a_1\rightarrow 1^{st}\ term, d\rightarrow \textrm{common difference}$

Plug in 3 for $a_1$ and 2 for $d$. This gives,

$a_{n}=3+(n-1)\times 2$

Therefore, the explicit formula to represent the given sequence is:

$a_{n}=3+2(n-1)$