Problem Breakdown: Consecutive Multiples of 2
We are asked to find the largest of five consecutive multiples of 2, given that their sum is 660.
Setting Up the Algebraic Equation
Let the five consecutive multiples of 2 be represented algebraically. If we denote the middle multiple as x, the sequence can be written as:
- x - 4
- x - 2
- x
- x + 2
- x + 4
The sum of these five consecutive multiples is given as 660. We can write this as an equation:
$ (x - 4) + (x - 2) + x + (x + 2) + (x + 4) = 660 $
Solving for the Middle Multiple
Simplify the equation by combining like terms:
$ 5x = 660 $
Now, solve for x by dividing both sides by 5:
$ x = \frac{660}{5} $
$ x = 132 $
So, the middle multiple of 2 is 132.
Finding the Largest Multiple
The five consecutive multiples are:
- 132 - 4 = 128
- 132 - 2 = 130
- 132
- 132 + 2 = 134
- 132 + 4 = 136
The largest number in this sequence is x + 4.
$ \text{Largest Number} = 132 + 4 = 136 $
The largest number among the five consecutive multiples of 2 is 136.
Similar Questions
- If the ratio of the 11th term of an AP to its 18th term is 2 : 3, find the ratio of the sum of its first five terms to the sum of its first 10 terms.
- The $10^{\text{th}}$ term of the Arithmetic Progression $2, 7, 12, \dots$ is:
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- What is the $50^{\text{th}}$ term of Arithmetic Progression 3, 8, 13, 18, 23, ........?
- The sum of all odd numbers between 0 and 52 is:
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- What is the value of k in the following Arithmetic progression?
$$15+13+11+9+ \dots +k = -105$$
Important Questions from Arithmetic Progression
If the nth term of a sequence is \(\frac{2 n+5}{7}\), then what is the sum of its first 140 terms?
What is the arithmetic mean of first 8 multiples of 13?
The average of five consecutive odd natural numbers is 27. The product of the first and fifth number is:
Find the sum of all the numbers between 100 to 200 which are divisible by 12.
In a garden, there are 6 daisy plants the first year. Each year, a gardener adds 3 new daisy plants the first year and loses 2 each year. He has 26 jasmine plants the first year and loses 2 each year. When will the number of daisy plants equal the number of jasmine plants after the first year?
