Advertisements
Advertisements
प्रश्न
Find the sum of all integers between 100 and 550, which are divisible by 9.
Advertisements
उत्तर
In this problem, we need to find the sum of all the multiples of 9 lying between 100 and 550.
So, we know that the first multiple of 9 after 100 is 108 and the last multiple of 9 before 550 is 549.
Also, all these terms will form an A.P. with the common difference of 9.
So here,
First term (a) = 108
Last term (l) = 549
Common difference (d) = 9
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
`549 = 108 + (n - 1)9
549 = 108 + 9n - 9
549 = 99 + 9n
Further simplifying,
450 = 9n
`n= 450/9`
n = 50
Now, using the formula for the sum of n terms,
`S_n =n/2[2a + (n -1)d]`
We get
`S_n = 50/2 [2(108) + (50 - 1)d]`
= 25[216 + (49)9]
= 25(216 + 441)
= 25(657)
= 16425
Therefore, the sum of all the multiples of 9 lying between 100 and 550 is `S_n= 16425`
संबंधित प्रश्न
The sum of three numbers in A.P. is –3, and their product is 8. Find the numbers
Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120
Find the sum of the following arithmetic progressions:
41, 36, 31, ... to 12 terms
Find the sum of the first 13 terms of the A.P: -6, 0, 6, 12,....
If `4/5 `, a, 2 are in AP, find the value of a.
If the sum of first n terms is (3n2 + 5n), find its common difference.
Choose the correct alternative answer for the following question .
In an A.P. 1st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....
If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero.
What is the sum of first 10 terms of the A. P. 15,10,5,........?
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 − S10)
Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....
For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?
Write the nth term of the \[A . P . \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]
The common difference of the A.P.
The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
Find the sum of first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively.
Find the sum of all the 11 terms of an A.P. whose middle most term is 30.
How many terms of the AP: –15, –13, –11,... are needed to make the sum –55? Explain the reason for double answer.
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 – n)..
Find:
- its first term and common difference
- sum of its first 25 terms
