Question

Given a series: 7,8,10,9,13,10,16,11, ?
Which number should come next ?
Options
a : 19
b : 18
c : 20
d : 16

Answer 1

Answer:

In this sequence 7 , 10 , 8 , 11 , 9 , 12 , ….. , the first term is 7 and the second one is 10 .if you observe the terms 7 and 10 , the second term 10 is obtained by adding 3 to the first term.

Like 7+3= 10.

Observe the second term 10 and the third term 8 . Here 2 is subtracted from the second term 10 , so it came 8 .

Like 10–2 =8 .

Observe 8 and 11 , here 3 is added to 8 to get 11 and for 11 and 9 , 2 is subtracted from 11 and so on.

So in the above sequence 3 and 2 are added and subtracted alternatively from preceeding term to get the next term .so if we move in this manner we get 10 as the seventh term in the above sequence.

Alternatively , In the above sequence you can observe at the odd places starting from 7 , all the other terms at the odd places can be obtained by just adding 1 to the preceeding term at the odd place and so for even place terms too. You might be wondering how This can be possible .here is the answer.

There are two AP series at odd places and at even places respectively. In every two side terms starting from first , we are adding 3 and subtracting 2 , so the next term at the odd place after the first two terms will be 1 added and so for at the even places too.

In this manner also we can get the required answer 10 at the seventh position.

So finally the sequence would be like the following.

7 ,10 ,8 ,11 ,9 ,12 ,10 ,13 ,11 ,14 , ……….