Question

The even natural numbers are divided into groups as (2), (4, 6), (8, 10,12), (14, 16,18,20) and so on. The sum of numbers in the 31st group is
A) 28908
B) 29822
C) 28512
D) 29424

Answer 1

Given :   The even natural numbers are divided into groups as (2), (4, 6), (8, 10,12), (14, 16,18,20) and so on.  

To Find : The sum of numbers in the 31st group  

Solution:

(2)  , ( 4 , 6) , ( 8 , 10 , 12) , ( 14 , 16 , 18 , 20 ) ......

Number of elements in 1st group = 1

in 2nd group = 2

is 31 st group   = 31

Element  in 30 groups = 1 + 2 + 3 +..............................+ 30

= (30)(31)/2

= 465

So number in group 31 st are from

466   to  465 + 31 = 496

As these are even number hence

2 * 466   , 2 * 467 , ......................................., 2 * 496

Sum = (n/2)(a + L)

Sum =  (31/2) (2 * 466 + 2 * 496)  

=29822

The sum of numbers in the 31st group is 29822

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