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The sum of five consecutive numbers is 260. The sum of the first and the last numbers is:
96
126
116
104
104
For any arithmetic progression or consecutive numbers, the average of the first and last numbers is equal to the average of all the numbers.
Sum of 5 consecutive numbers = 260
Sum=n├ЧAverage
For any arithmetic progression or consecutive numbers, the average of the first and last numbers is equal to the average of all the numbers.
Students often try to find all five individual numbers by solving an algebraic equation, which is time-consuming and prone to calculation errors.
Step 1: Understand the properties of consecutive numbers
Let the five consecutive numbers be xтИТ2, xтИТ1, x, x+1, and x+2. The sum of these numbers is given as 260.
(xтИТ2)+(xтИТ1)+x+(x+1)+(x+2)=260
Step 2: Solve for the middle number x
Simplifying the left-hand side gives 5x=260. Dividing by 5 gives the middle number.
5x=260тЯ╣x=5260тАЛ=52
Step 3: Find the first and last numbers
The first number is xтИТ2=52тИТ2=50, and the last number is x+2=52+2=54.
First=50,Last=54
Step 4: Calculate the sum of the first and last numbers
Adding the first and the last number together:
50+54=104
D is correct because the sum of the first and the last numbers of five consecutive numbers whose sum is 260 is 104.
For any arithmetic progression with an odd number of terms, the sum of the first and last terms is always equal to twice the middle term (or twice the average).
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