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
Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.
The sum of the first p, q, r terms of an A.P. are a, b, c respectively. Show that `\frac { a }{ p } (q – r) + \frac { b }{ q } (r – p) + \frac { c }{ r } (p – q) = 0`
Ramkali saved Rs 5 in the first week of a year and then increased her weekly saving by Rs 1.75. If in the nth week, her week, her weekly savings become Rs 20.75, find n.
Which term of the A.P. 121, 117, 113 … is its first negative term?
[Hint: Find n for an < 0]
Find the sum of the first 40 positive integers divisible by 5
Find the sum of the first 15 terms of each of the following sequences having the nth term as
bn = 5 + 2n
The 4th term of an AP is 11. The sum of the 5th and 7th terms of this AP is 34. Find its common difference
The sum of three numbers in AP is 3 and their product is -35. Find the numbers.
If the ratio of sum of the first m and n terms of an AP is m2 : n2, show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1) ?
The Sum of first five multiples of 3 is ______.
Choose the correct alternative answer for the following question .
15, 10, 5,... In this A.P sum of first 10 terms is...
Find the sum of the first 15 terms of each of the following sequences having nth term as xn = 6 − n .
Ramkali would need ₹1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved ₹50 in the first month of this year and increased her monthly saving by ₹20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?
The sum of first six terms of an arithmetic progression is 42. The ratio of the 10th term to the 30th term is `(1)/(3)`. Calculate the first and the thirteenth term.
In an A.P. sum of three consecutive terms is 27 and their products is 504. Find the terms. (Assume that three consecutive terms in an A.P. are a – d, a, a + d.)
Write the formula of the sum of first n terms for an A.P.
Find the sum of natural numbers between 1 to 140, which are divisible by 4.
Activity: Natural numbers between 1 to 140 divisible by 4 are, 4, 8, 12, 16,......, 136
Here d = 4, therefore this sequence is an A.P.
a = 4, d = 4, tn = 136, Sn = ?
tn = a + (n – 1)d
`square` = 4 + (n – 1) × 4
`square` = (n – 1) × 4
n = `square`
Now,
Sn = `"n"/2["a" + "t"_"n"]`
Sn = 17 × `square`
Sn = `square`
Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is `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?
A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment
The sum of all odd integers between 2 and 100 divisible by 3 is ______.
