Advertisements
Advertisements
प्रश्न
Find the sum of the integers between 100 and 200 that are not divisible by 9.
Advertisements
उत्तर
The sum of the integers between 100 and 200 which is not divisible by 9 = (sum of total numbers between 100 and 200) – (sum of total numbers between 100 and 200 which is divisible by 9) ...(i)
Total numbers between 100 and 200 is 101, 102, 103,..., 199
Here, a = 101, d = 102 – 101 = 1 and an = l = 199
`\implies` 199 = 101 + (n – 1)1 ...[∵ an = l = a + (n – 1)d]
`\implies` (n – 1) = 98
`\implies` n = 99
Sum of terms between 100 and 200,
Sn = `n/2[2a + (n - 1)d]`
`\implies` S99 = `99/2[2(101) + (99 - 1)1]`
= `99/2[202 + 98]`
= `99/2 xx 300`
= 99 × 150
= 14850
From equation (i), sum of the integers between 100 and 200 which is not divisible by 9
= 14850 – 1683 ...[From part (i)]
= 13167
Hence, the required sum is 13167.
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 the following arithmetic progressions:
a + b, a – b, a – 3b, ... to 22 terms
How many two-digits numbers are divisible by 3?
How many three-digit natural numbers are divisible by 9?
Find the first term and common difference for the A.P.
0.6, 0.9, 1.2,1.5,...
In an A.P. the first term is – 5 and the last term is 45. If the sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?
If `4/5`, a, 2 are three consecutive terms of an A.P., then find the value of a.
Find the common difference of an A.P. whose first term is 5 and the sum of first four terms is half the sum of next four terms.
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?
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 ______.
