Question

What is the sum of all the even numbers from 20 to 70

Answer 1

22,24,26,28,32,34,36,38,40,42,44,46,48,52,54,56,58,60,62,64,66,68

Answer 2

the even numbers starting from 20 to 70 when being add form an A.P

the first term being 20 the last term 70 and common difference = 2

Let us first find the number of terms in it

suppose 70 is the nth term .

nth term of A.P= a+ ( n-1) d here a= 20 and d = 2

70 = 20 +( n-1) * 2

70-20 = (n-1)*2

50= (n-1)*2

50/2 = n-1

25 = n-1

25 +1 = n

26 = n

let us now find sum of these 26 terms

sum formula for n terms = n ( 2a+ ( n-1) d)

-------------------------

2

26 ( 2* 20 + ( 26-1)* 2)

--------------------------------------------------

2

13 ( 40 + 25 * 2)

13 ( 40 +50 )

13 ( 90 )

1170 Answer.