Question

What is the next term in the series $ 8,12,24,60 $ ?

Answer 1

Hint: There are many types of series present in mathematics. They can also be called progressions. This means that each term of the progression or series advances using a specific formula; it may be that something is added to it or something is multiplied. It can be of any formula. In this question we have to find the rule of the given series and then predict the next number in the series.

Complete step-by-step answer:
The basic method of determining the rule a series follows is to compare two consecutive terms.
We are given the series
 $ 8,12,24,60 $
The difference between the second term and the first term is given by :
 $ \Rightarrow 12 - 8 = 4 $
The difference between the third and the second term is given by:
 $ \Rightarrow 24 - 12 = 12 $
The difference between the fourth and the third term is given by:
 $ \Rightarrow 60 - 24 = 36 $
On comparing the difference of the consecutive terms in the series we get as,
 $ 4,12,36 $
As we can see this is a geometric progression, that the next term is obtained by multiplying $ 3 $ to the previous term. Like:
 $
   \Rightarrow 4 \times 3 = 12 \\
   \Rightarrow 12 \times 3 = 36 \;
 $
Thus the next term would be
 $ \Rightarrow 36 \times 3 = 108 $
So the next term in the original series would be $ 108 $ more than the previous term. Since the last term in the original series is given by $ 60 $ . The next term in the series would be ,
 $ \Rightarrow 60 + 112 $
 $ \Rightarrow 172 $
Thus the next term in the series is $ 172 $
So, the correct answer is “172”.

Note: The two main types of progression in mathematics are arithmetic and geometric progression.
In arithmetic progression each consecutive term in the A.P is incremented by a common factor $ d $ . So the terms of A.P. with the first term as $ a $ is as follows:
 $ a,a + d,a + 2d,a + 3d...... $
On the other hand in geometric progression each term is multiplied by a common factor $ d $ to obtain its consecutive term, so the terms of G.P with the first term as $ a $ would be,
 $ a,ar,a{r^2},a{r^3}...... $