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

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.

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

x= 149. 24+7=31. 180-31=149

your welcome

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is