Advertisements
Advertisements
प्रश्न
Find the sum of all even numbers from 1 to 250.
Advertisements
उत्तर
The even numbers from 1 to 250 are 2, 4, 6, 8, ............, 250
And the last even number is = 250
∴ an = 250, a = 2 and d = 2
∴ an = a + (n – 1)d
∴ 250 = 2 + (n – 1)2
∴ 250 = 2 + 2n – 2
∴ 2n = 250
∴ n = `250/2` = 125
From 1 to 250, there are 125 even numbers.
Since, we know `S_n = n/2 [a + a_n]`
∴ The sum of 125 even numbers
`S_125 = 125/2 [2 + 250]`
= `125/2 xx 252`
= 125 × 126
= 15,750
As a result, the total of all even numbers from 1 to 250 is 15,750.
APPEARS IN
संबंधित प्रश्न
In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms.
How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?
In an AP given an = 4, d = 2, Sn = −14, find n and a.
Find the sum of the following arithmetic progressions:
`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`, .....to n terms
If the 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.
Which term of the AP ` 5/6 , 1 , 1 1/6 , 1 1/3` , ................ is 3 ?
The sum of the first n terms of an AP is (3n2+6n) . Find the nth term and the 15th term of this AP.
The nth term of an AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?
Choose the correct alternative answer for the following question .
First four terms of an A.P. are ....., whose first term is –2 and common difference is –2.
For an given A.P., t7 = 4, d = −4, then a = ______.
Simplify `sqrt(50)`
A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.
Write the expression of the common difference of an A.P. whose first term is a and nth term is b.
The sum of n terms of an A.P. is 3n2 + 5n, then 164 is its
Find the sum of 12 terms of an A.P. whose nth term is given by an = 3n + 4.
The sum of all odd integers between 2 and 100 divisible by 3 is ______.
Calculate the sum of 35 terms in an AP, whose fourth term is 16 and ninth term is 31.
Find the middle term of the AP. 95, 86, 77, ........, – 247.
