Find the sum of all even integers from 2 to 281.
19740
19740 is correct.
The even integers from 2 to 281 are 2, 4, 6, …, 280 (281 is odd, so the last even number is 280). They form an arithmetic progression with first term 2 and common difference 2.
Number of terms: \(n = \dfrac{280}{2} = 140\)
Sum: \(S = \dfrac{n}{2}(a + l) = \dfrac{140}{2}(2 + 280) = 70 \times 282 = 19740\)
Hence, the sum of all even integers from 2 to 281 is 19740.
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.
- What is the $50^{\text{th}}$ term of Arithmetic Progression 3, 8, 13, 18, 23, ........?
- The sum of the first 12 multiples of 6 is:
- If the sum of five consecutive multiples of 2 is 660, then find the largest number.
- What is the sum of the first 12 multiples of 4?
- The tenth term of the sequence 2, 5, 8, 11, ......will be:
- The $10^{\text{th}}$ term of the Arithmetic Progression $2, 7, 12, \dots$ is:
- The sum of all odd numbers between 0 and 52 is:
- What is the sum of the first 25 odd numbers?
- In the series 11, 19, 27, 35, 43, ....... which of the following will NOT be a number of the series?
Important Questions from Arithmetic Progression
If the arithmetic mean of a, b, c is \(\rm \frac M 3\) and \(\rm \frac{1}{a} + \frac{1}{b} = -\frac{1}{c} \) , then the arithmetic mean of a 2, b 2, c 2 is
A person saves Rs. 1000 more than he did the previous year. If he saves Rs. 2000 in the first year, in how many years will he save Rs. 170000?
How many natural numbers lie between 3 and 200 which are divisible by 7?
The arithmetic mean of 16 student's scores is 320. Find the sum of these scores.
How many three-digit numbers are divisible by 5?
