Identifying the Sequence of Multiples
The question asks for the sum of the first 12 multiples of 4. These multiples form a sequence:
- 4 x 1 = 4
- 4 x 2 = 8
- 4 x 3 = 12
- ...
- 4 x 12 = 48
This sequence is an arithmetic progression (AP) where:
- The first term ($a$) is 4.
- The common difference ($d$) is 4.
- The number of terms ($n$) is 12.
- The last term ($l$) is 48.
Calculating the Sum using AP Formula
The sum ($S_n$) of an arithmetic progression can be calculated using the formula:
$ S_n = \frac{n}{2}(a + l) $
Substitute the values:
$ S_{12} = \frac{12}{2}(4 + 48) $
$ S_{12} = 6 \times 52 $
$ S_{12} = 312 $
Alternatively, using the formula $S_n = \frac{n}{2}(2a + (n-1)d)$:
$ S_{12} = \frac{12}{2}(2 \times 4 + (12-1) \times 4) $
$ S_{12} = 6(8 + 11 \times 4) $
$ S_{12} = 6(8 + 44) $
$ S_{12} = 6 \times 52 $
$ S_{12} = 312 $
Final Answer
The sum of the first 12 multiples of 4 is 312.
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.
- If the sum of five consecutive multiples of 2 is 660, then find the largest number.
- The $10^{\text{th}}$ term of the Arithmetic Progression $2, 7, 12, \dots$ is:
- The sum of the first 12 multiples of 6 is:
- 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:
- The tenth term of the sequence 2, 5, 8, 11, ......will be:
- What is the sum of the squares of all two-digit numbers each of which is completely divisible by 4?
- What is the sum of the first 25 odd numbers?
- 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?
