Advertisements
Advertisements
प्रश्न
Find the sum of all integers between 50 and 500, which are divisible by 7.
Advertisements
उत्तर
In this problem, we need to find the sum of all the multiples of 7 lying between 50 and 500.
So, we know that the first multiple of 7 after 50 is 56 and the last multiple of 7 before 500 is 497.
Also, all these terms will form an A.P. with the common difference of 7.
So here,
First term (a) = 56
Last term (l) = 497
Common difference (d) = 7
So, here the first step is to find the total number of terms. Let us take the number of terms as n.
Now, as we know,
`a-n = a+ (n -1)d`
So, for the last term,
497 = 56 + (n -1)7
497 = 56+ 7n - 7
497 = 49 +7n
497 - 49 = 7n
Further simplifying
448 = 7n
`n = 448/7`
n = 64
Now, using the formula for the sum of n terms,
`S_n = n/2 [2a + (n -1)d]`
For n = 64 we get
`S_n = 64/2 [2(56) + (64 - 1) 7]`
= 32 [112 + (63)7]
= 32(1123 + 441)
= 32(112 + 441)
= 32(553)
= 17696
Therefore the sum of all the multiples of 7 lying betwenn 50 and 500 is `S_n = 17696`
APPEARS IN
संबंधित प्रश्न
The ratio of the sum use of n terms of two A.P.’s is (7n + 1) : (4n + 27). Find the ratio of their mth terms
If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms.
Which term of the AP 21, 18, 15, …… is -81?
Find the 6th term form the end of the AP 17, 14, 11, ……, (-40).
Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.
Find four numbers in AP whose sum is 8 and the sum of whose squares is 216.
Write the next term for the AP` sqrt( 8), sqrt(18), sqrt(32),.........`
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
Kargil’s temperature was recorded in a week from Monday to Saturday. All readings were in A.P. The sum of temperatures of Monday and Saturday was 5°C more than sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was –30° celsius then find the temperature on the other five days.
Simplify `sqrt(50)`
Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .
Write the common difference of an A.P. whose nth term is an = 3n + 7.
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.
Q.6
The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
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))`.
Rohan repays his total loan of ₹ 1,18,000 by paying every month starting with the first installment of ₹ 1,000. If he increases the installment by ₹ 100 every month, what amount will be paid by him in the 30th installment? What amount of loan has he paid after 30th installment?
