Question

A sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence is known as

• A. geometric series
• B. arithmetic progression
• C. arithmetic series
• D. geometric sequence

Answer 1

The correct option is D geometric sequence

A sequence of number, $a_1+a_2+......a_n$ quotient of any two successive number is a constant,

$\frac{a_2}{a_1}=\frac{a_3}{a_2}=........=\frac{a_n}{a_{n-1}}=$common ratio $\left(r\right)$

So we can write

$a_1+a_{1}r+a_{2}r+a_{3}r.......a_{n-1}r=a_1+a_{1}r+a_1{r}^2..........a_{n-2}{r}^2$

and in the end in terms of $a_1$

$=a_1+a_{1}r+a_1{r}^2+a_1{r}^3.........a_1{r}^{n-1}$

We can clearly say this series is in $GP$.

Answer $\left(D\right)$