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Levart [38]
3 years ago
6

What is the sum of all even numbers between 1 and 1000

Mathematics
1 answer:
weeeeeb [17]3 years ago
4 0
There are 500 even numbers from 1 to 1000 starting with 2 and ending with 998. The sequence of even numbers is an arithmetic sequence with a common difference of 2. Using the equation for the arithmetic series,

                                       S = (a1 + an)(n/2)
and substituting, 
                                     
                                        S = (2 + 998)(500/2)
we get, 

                                        S = 250,000

Therefore, the sum of all even numbers between 1 and 1000 is 250,000.

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If the mean of A and B is 20, the mean of B and C is 24 and the mean of A,B and C is 18.What is the mean of A and C?
Zielflug [23.3K]

Answer:

the mean of A and C is 10

Step-by-step explanation:

Given;

mean of A and B = 20

mean of B and C = 24

mean of A, B and C = 18

\frac{A + B}{2} = 20\\\\A+ B = 40 ---- (1)\\\\\frac{B + C}{2} = 24\\\\B+ C = 48----(2)\\\\\frac{A+ B+ C}{3} = 18\\\\A+ B+ C= 54---(3)\\\\From (1); \ A = 40 - B\\\\From(2); \ C = 48 - B\\\\\Substitute \ the \ values \ of \ A \ and \ C \ into \ (3)\\\\(40-B) + B + (48-B) = 54\\\\simplify;\\\\(40 + 48) + (B-B-B)= 54\\\\88 -B = 54\\\\-B = 54-88\\\\-B = -34\\\\B = 34

Recall; A = 40 - B

           A = 40 - 34

           A = 6

Also, C = 48 - B

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Therefore, the mean of A and C is calculated as;

= \frac{A + C}{2} \\\\= \frac{6 + 14}{2} \\\\= 10

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