Advertisements
Advertisements
प्रश्न
Find the sum of all multiples of 9 lying between 300 and 700.
Advertisements
उत्तर
The multiples of 9 lying between 300 and 700 are 306, 315,………, 693.
This is an AP with a = 306,d = 9 and l = 693.
Suppose these are n terms in the AP. Then,
an = 693
⇒ 306+ (n-1) × 9 = 639 [an = a + (n-1) d]
⇒ 9n + 297 = 693
⇒ 9n = 693 - 297 = 396
⇒ n=44
∴ Required sum = `44/2 (306 = 693) [s_n = n/2 (a+1)]`
= 22× 999
= 21978
Hence, the required sum is 21978.
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.
Find the sum of first 20 terms of the following A.P. : 1, 4, 7, 10, ........
Find the sum of the following APs.
`1/15, 1/12, 1/10`, ......, to 11 terms.
Find the sum given below:
`7 + 10 1/2 + 14 + ... + 84`
Find the sum of first 40 positive integers divisible by 6.
Find the sum of the following arithmetic progressions:
1, 3, 5, 7, ... to 12 terms
Find the sum of the first 15 terms of each of the following sequences having the nth term as
yn = 9 − 5n
The sum of n natural numbers is 5n2 + 4n. Find its 8th term.
Determine k so that (3k -2), (4k – 6) and (k +2) are three consecutive terms of an AP.
If 18, a, (b - 3) are in AP, then find the value of (2a – b)
If the sum of first n terms is (3n2 + 5n), find its common difference.
The sum of the first n terms in an AP is `( (3"n"^2)/2 +(5"n")/2)`. Find the nth term and the 25th term.
The next term of the A.P. \[\sqrt{7}, \sqrt{28}, \sqrt{63}\] is ______.
Choose the correct alternative answer for the following question .
In an A.P. first two terms are –3, 4 then 21st term is ...
Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.
Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
The given terms are 2k + 1, 3k + 3 and 5k − 1. find AP.
Find the sum of three-digit natural numbers, which are divisible by 4.
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]
Three numbers in A.P. have the sum of 30. What is its middle term?
