Hey,

if we look at the series then the numbers are added as 2,3,4,5 and so....with  the preceding numbers, that is 1,3,6,10

that is,

1+2=3

3+3=6

6+4=10

10+5=15

15+6=21

21+7=28 and so on....

thus the required series will be 1,3,6,10,15,21,28... and so on.

Which is the required series.

I hope this helps.

Hello,

The given series is 1, 3, 6, 10,...

The difference between the first and second terms is 3-1 =2.The difference between the third and second terms is 6-3 = 3.Similarly the difference between the fourth and third term is 10-6 = 4.

So the difference between two consecutive numbers follows a pattern 2, 3, 4, 5 ,6..

So the difference between the fifth and fourth terms will be  5.Therefore the fifth term will be 10+5 = 15.

The series will be 1, 3, 6, 10, 15, 21, 28,...

Hope this helps!!!