Advertisements
Advertisements
प्रश्न
Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.
Advertisements
उत्तर
Since, multiples of 2 as well as of 5 = LCM of (2, 5) = 10
But multiples of 2 as well as 5 from 1 to 500 is 10, 20, 30,..., 500.
∴ a = 10, d = 10, an = l = 500
∵ an = a + (n – 1)d = l
⇒ 500 = 10 + (n – 1)10
⇒ 490 = (n – 1)10
⇒ n – 1 = 49
⇒ n = 50
∵ Sn = `n/2(a + l)`
⇒ S50 = `50/2(10 + 500)`
= `50/2 xx 510`
= 50 × 255
= 12750
APPEARS IN
संबंधित प्रश्न
The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
Find the sum given below:
–5 + (–8) + (–11) + ... + (–230)
In an AP, given a = 7, a13 = 35, find d and S13.
In an AP, given a = 2, d = 8, and Sn = 90, find n and an.
A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5, 1.0 cm, 1.5 cm, 2.0 cm, .... as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take `pi = 22/7`)
[Hint: Length of successive semicircles is l1, l2, l3, l4, ... with centres at A, B, A, B, ... respectively.]
If 4 times the 4th term of an A.P. is equal to 18 times its 18th term, then find its 22nd term.
What is the 5th term form the end of the AP 2, 7, 12, …., 47?
For an given A.P., t7 = 4, d = −4, then a = ______.
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
The sum of third and seventh term of an A. P. is 6 and their product is 8. Find the first term and the common difference of the A. P.
Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + . . . . . . . . . .\]
The first term of an A.P. is p and its common difference is q. Find its 10th term.
If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?
x is nth term of the given A.P. an = x find x .
Find second and third terms of an A.P. whose first term is – 2 and the common difference is – 2.
Write the formula of the sum of first n terms for an A.P.
Find t21, if S41 = 4510 in an A.P.
If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be ______.
The sum of all odd integers between 2 and 100 divisible by 3 is ______.
If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is `(q + r - 2p) xx ((p + r))/(2(q - p))`.
