Question

The sum all even natural numbers between 1 and 31 is:

Answer 1

REQUIRED SUM=(2+4+6+8+........+30)
(2+4+6+8+.............+2n)=n(n+1)
here, 2n=30
n=30/2=15
15(15+1)=15*16=240

Answer 2

Answer:

Sum of all even natural numbers between 1 and 31 = 240

Step-by-step explanation:

2,4,6,8,....,30 are even natural numbers between 1 and 31are in A.P

Here,

First term (a) = 2,

Common difference (d) =a2-a1

= 4-2

= 2

Number of terms (n) = 15

Last term (l) = 30

Now,

Sum of n terms =

$S_{n} = \frac{n}{2}(a+l)$

$\implies S_{15}=\frac{15}{2}(2+30)$

$\implies S_{15}=\frac{15}{2}\times 32$

= $15 \times 16$

= $240$

Therefore,

Sum of all even natural numbers between 1 and 31 = 240

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