Advertisements
Advertisements
Question
Find the sum of all even numbers from 1 to 250.
Advertisements
Solution
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
RELATED QUESTIONS
A ladder has rungs 25 cm apart. (See figure). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2 `1/2` m apart, what is the length of the wood required for the rungs?
[Hint: number of rungs = `250/25+ 1`]
Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Find the sum of all integers between 100 and 550, which are divisible by 9.
Find the sum of the first 15 terms of each of the following sequences having the nth term as
yn = 9 − 5n
If the sum of first n terms is (3n2 + 5n), find its common difference.
The sum of the first n terms of an AP is `((5n^2)/2 + (3n)/2)`. Find the nth term and the 20th term of this AP.
Write an A.P. whose first term is a and the common difference is d in the following.
a = 10, d = 5
Find the first term and common difference for the A.P.
`1/4,3/4,5/4,7/4,...`
If first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is \[\frac{\left( a + c \right) \left( b + c - 2a \right)}{2\left( b - a \right)}\].
If the 10th term of an A.P. is 21 and the sum of its first 10 terms is 120, find its nth term.
If Sr denotes the sum of the first r terms of an A.P. Then , S3n: (S2n − Sn) is
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
The nth term of an A.P., the sum of whose n terms is Sn, is
If Sn denote the sum of n terms of an A.P. with first term a and common difference dsuch that \[\frac{Sx}{Skx}\] is independent of x, then
Q.17
How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78? Explain the double answer.
Determine the sum of first 100 terms of given A.P. 12, 14, 16, 18, 20,......
Activity :- Here, a = 12, d = `square`, n = 100, S100 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]`
S100 = `square/2 [24 + (100 - 1)"d"]`
= `50(24 + square)`
= `square`
= `square`
In a ‘Mahila Bachat Gat’, Sharvari invested ₹ 2 on first day, ₹ 4 on second day and ₹ 6 on third day. If she saves like this, then what would be her total savings in the month of February 2010?
The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.
