# math

what is the sum of all consecutive numbers from 101 to 200, those two numbers inclusive?

Halfway between, is 150. Then add 149+151,thence 148+152, and so on till 101+199. Each instance you have 300. So it seems to me...

Sum= 200 + 150 + 300*N, where N is the number of pairs you added. You should be able to figure that out.

There is another method, of course: Use the formula for the sum of an arithmetic sequence. It works well here.

The sum of the set of consecutive numbers from "a" to "b" is given by S = a(a + 1)/2 - b(b - 1)/2.

If the smallest number of the group of 50 is 1997, the largest number is 1997 + (50 - 1) = 2046.

Their sum is S = 2046(2047)/2 - 1997(1996)/2 = 101,075 or
...................S = [2046^2 + 2046 - 1997^2 + 1997]/2 = 101,075 or
...................S = (1997 + 2046)(2046 - 1997 + 1)/2 = 101.075.

The equivalent sum of another 25 consecutive numbers, the smallest of which is "x", derives from
(x + 24)(x + 25)/2 - x(x - 1)/2 = 101,075

Expanding, x^2 = 49x + 600 - x^2 + x = 202,150.

Thus, 49x = 210,550 making x = 4031.

The group of 25 conscutive numbers is therefore 4031 - 4055.

Their sum is 4055(4056)/2 - 4031(4030)/2 = 101,075.

1. 👍
2. 👎
3. 👁

## Similar Questions

1. ### Math

The sum of 3 consecutive odd natural numbers is 69. Find the prime number out of these numbers.

2. ### Math

the sum of 5 consecutive whole numbers is 2005. what is the sum of all the digits of these 5 numbers

3. ### Math

The sum of three consecutive odd numbers is 615? Find the numbers.

4. ### maths

can you replace the stars with figures **** x 3 ______ ***** the whole calculation uses each of the digits 0-9 once and once only the 4 figure number contains three consecutive numbers which are not in order. the third digit is

1. ### Math

find the sum of the numbers from 1 to 200 inclusive

2. ### math

Three consecutive even numbers have a sum between 84 and 96. a. Write an inequality to find the three numbers. Let n represent the smallest even number. b. Solve the inequality

3. ### geometry

HELP.... In a certain lottery, 3 numbers between 1 and 9 inclusive are drawn. These are the winning numbers. How many different selections are possible? Assume the order in which the numbers are drawn is not important. Answer

4. ### Math

Two consecutive even whole numbers are selected. The difference between the reciprocals of the two numbers is 1/60. Determine the numbers.

1. ### Math

The sum of two numbers is 39. Twice the first number plus three times the second number is 101. Find the numbers.

2. ### Algebra

The sum of three consecutive odd numbers is 39. What are the smallest of these numbers?

3. ### math

The sum of two consecutive numbers is n+1. What are the numbers?

4. ### Algebra

Eleven numbers with the sum 105 are written on the circle. The sum of any two consecutive numbers is not smaller than 18. Find the least possible value of N, so that each number on the circle is not greater than N, for any set of