The sum of next two numbers in the pattern 3, 10, 32, 99, _____, _____ is

To find the sum of the next two numbers in the pattern 3, 10, 32, 99, we first need to determine the rule governing the sequence.

Let the terms of the sequence be represented by $a_n$, where:

$a_1=3$

$a_2=10$

$a_3=32$

$a_4=99$

Let's analyze the relationship between consecutive terms:
- To get from the 1st term to the 2nd term:
$3\times 3+1=10$
- To get from the 2nd term to the 3rd term:
$10\times 3+2=32$
- To get from the 3rd term to the 4th term:
$32\times 3+3=99$

We can see that the pattern to find the next term is to multiply the current term by 3 and add an increasing integer ($1,2,3,...$). The general recursive formula is:

$a_{n+1}=3a_n+n$

Now, let's use this rule to calculate the next two terms of the sequence.

The 5th term ($a_5$) is:
$a_5=3\times a_4+4$
$a_5=3\times 99+4$
$a_5=297+4=301$

The 6th term ($a_6$) is:
$a_6=3\times a_5+5$
$a_6=3\times 301+5$
$a_6=903+5=908$

So, the next two numbers in the pattern are 301 and 908.

Finally, we find the sum of these next two numbers:
$\text{Sum}=301+908=1209$

Therefore, the correct option is 1209.