Question

What is the common ratio of the geometric sequence below?

Answer 1

`\textbf{Option C - $0.1$}\\`

Explanation:

`\textup{A geometric series is given by}\\$ a, ar, ar^2, ar^3,. . . , ar^(n-1), ar^n $ \\\textup{\textbf{Geometric progression or GP is a sequence of numbers in which the next number in the sequence is obtained by multiplying a number to the previous number in the sequence.}}\\`

`\textup{This number is constant through out the sequence and is denoted by $r$. it is given by $r = (ar^n)/(ar^(n-1))$} \\`

`\textup{Here, the given sequence is: $70, 7, 0.7,...$}\\`

`$i.e., a = 70, ar = 7$\\`

`\textup{Hence, $r = (ar)/(a) = (7)/(70)$ }\\`

`$= (1)/(10) = 0.1$`