Question

7, 38, 75, 116, 159, __________

Answer 1

Given:

We have given the series with terms 7,38,75,116,159.

To Find:

We have to find the next term of the given series?

Step-by-step explanation:

• Series:

• Series is the number of the different things or anything of the same class placed in the one after one format. In any of the series a particular format is being used bt the different terms.

• The format for the different terms of the series will always same.

• Now we have given the series with terms 7,38,75,116,159.

• First of all we try to find to establish and particular format is followed here by the given series

• By observing the given terms we getDifference of  first term and second term is 31 and Difference of second term and third term is37 Also difference of third term and fourth term is 41.

         Hence we get the pattern which is incese in prime number

          $38-7 =31\\75-38=37\\116-75=41\\159-116=43$

Thus, the next term is 159+47=206.

Hence , the next term will be 206 .

Answer 2

Answer:

7,38,75,116,159,206

Step-by-step explanation:

In the given series, the first number is 7

7+ 31 = 38

38+ 37 = 75

75+ 41 = 116

116+ 43 = 159

Here, 31,37,41 and 43 are consecutive prime numbers.

47 is the next prime number after the number 43

So the next number in the series will be:

159+47 = 206

So the series is :

7,38,75,116,159,206