Question

Find next number of the series:- \[120,15,105,17.5,87.5,?\]
A.\[18.5\]
B.\[19.5\]
C.\[21.875\]
D.\[17.5\]
E.\[90\]

Answer 1

Hint: Here, we have to find the next number in the series by finding the relation between the first and second term, third and fourth term, fifth term, after which we have to find the sixth term.

Complete step-by-step answer:
We are taking the first term 120.
The First term should be divided by the number 8. Therefore, we have
\[ \Rightarrow \dfrac{{120}}{8} = 15\]
This arrives at the second term.
The Second term should be multiplied by the number 7. So, we have
\[ \Rightarrow 15 \times 7 = 105\]
This arrives at the third term.
The third term should be divided by the number 6. So, we have
\[ \Rightarrow \dfrac{{105}}{6} = 17.5\]
This arrives at the fourth term.
The fourth term should be multiplied by the number 5. Therefore, we have
\[ \Rightarrow 17.5 \times 5 = 87.5\]
This arrives at the fifth term.
So, to find the sixth term, the fifth term should be divided by the number 4. So, we get
\[ \Rightarrow \dfrac{{87.5}}{4} = 21.875\]
Therefore, the sixth term of the series is \[21.875\].

Note: An easy method to solve the number series is we have to check whether the series is in ascending order or descending order. If the series is in ascending order, then the number has to be added or multiplied by any number from the first term. If the series is in descending order, then the number has to be subtracted or divided by any number from the first term. The given series is called the geometric series. This type of series is based on the ascending or descending order of numbers and each continued number is obtained by multiplication or division of the previous number.