Question

What Is The Sum Of All Even Integers Between 10 And 50

Answer 1

even number b/w 10&50 are

12,14,16..............50

a=12

d=a2-a1

=14-12

=2

an=50

a+(n-1)d=50

12+(n-1)2=50

12+2n-2=50

10+2n=50

2n=50-10

2n=40

n=40/2

n=20

sn=n/2(a+an)

=20/2(12+50)

=10(62)

=620

Answer 2

Sum of All Even Integers between 10 and 50 is 570

Given problem:

What Is The Sum Of All Even Integers Between 10 And 50

Solution:

All Even integers between 10 to 50 = {12, 14, 16 ... 48 }  

Here the number sequence is in Arithmetic Sequence  

where first term a = 12 and common difference d = 2

Last term of the sequence = 48

As we know nth term in AP = a+(n-1)d

Let n be the last term then, a+(n-1)d = 48

⇒ 12 + (n-1)2 = 48

⇒ (n-1)2 = 36

⇒ (n-1) = 18

⇒ n = 19

We know that sum of n terms in AP,  Sn = n/2 × [a₁+a$_{n}$]

Sum of 19 terms, S₁₉ = 19/2 × [12+48]  

⇒ 19/2 × [60]  

⇒ 19 (30) = 570

Therefore, Sum of All Even Integers between 10 and 50 = 570

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