Question

Write an explicit formula for an nth term of the sequence 7, 35, 175,....

Answer 1

hello

to write an explicit formula, we have to determine what type of sequence is it

7, 35, 17

this is clearly a geometric progression with values of

first term = 7

common ratio = 5

the explicit formula of a geometric progression is given as

`\begin{gathered} a_n=a\cdot r^((n-1))^{} \\ n=\text{nth term} \\ a=\text{first term} \\ r=\text{common ratio} \end{gathered}`

now let's substitute the variables into the equation

`\begin{gathered} a_n=a\cdot r^((n-1)) \\ a_n=7\cdot5^((n-1)) \\ a_n=35^((n-1)) \end{gathered}`

the equation above is the explicit formula for the sequence