Question

In a sequence 1,3,6,10......... the next two terms are *




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Answer 1

Answer:

the next two terms are 15 and 21

Answer 2

Answer:

In the given series :

1, 3, 6, 10 , .  .  .  .

The next two terms are  15, and 21 respectively.

Step-by-step explanation:

The difference between 1st and 2nd term = 3 - 1 = 2

The difference between 2rd and 3rd term = 6 - 3 = 3

The difference between 3rd and 4th term = 10 - 6 = 4

We observe that the difference between 2 consecutive terms increases by 1 at every step.

so,

The difference between 4th and 5th term = 5

=> $T_{5} - T_{4} = 5$

=> $T_{5}$ - 10 = 5

=> $T_{5}$ = 15

The difference between 5th and 6th term = 6

=> $T_{6} - T_{5}$ = 6

=> $T_{6}$ - 15 = 6

=>  $T_{6}$ = 6 + 15

=> $T_{6}$ = 21