What is the sum of the first 104 consecutive even numbers

Let  x  (x+1)   (x+2)   (x+3)    be the four consecutive integers.

Step-by-step explanation:

Their sum:

  x  + (x+1) + (x+2) + (x+3)  =  104

   4x + 6 = 104                    [collect like terms]

    4x = 98                [subtract 6 from both sides]

     x  = 27                [divide both sides by 4]

     x= 24.5   [rats!  that's not an integer !]

What does that mean -- Well, there are not four consecutive integers whose sum is 104.

Here are some close ones:

    24+ 25 + 26 + 27 = 102

    25 + 26 + 27 + 28  =  106

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh