Advertisements
Advertisements
Question
How many three-digit numbers are divisible by 9?
Advertisements
Solution
The three-digit numbers divisible by 9 are 108, 117, 126,...., 999.
Clearly, these number are in AP.
Here. a = 108 and d = 117 – 108 = 9
Let this AP contains n terms. Then.
an = 999
⇒ 108 + (n-1) × 9 = 999 [an = a + (n-1) d ]
⇒ 9n + 99 =999
⇒ 9n = 999 -99=900
⇒ n = 100
Hence: there are 100 three-digit numbers divisible by 9.
APPEARS IN
RELATED QUESTIONS
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 9th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Find the sum of first 15 multiples of 8.
A contract on a construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs. 200 for the first day, Rs. 250 for the second day, Rs. 300 for the third day, etc., the penalty for each succeeding day being Rs. 50 more than for the preceding day. How much money does the contractor have to pay as a penalty if he has delayed the work by 30 days.
Find the 12th term from the end of the following arithmetic progressions:
3, 5, 7, 9, ... 201
Find the sum 25 + 28 + 31 + ….. + 100
Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.
How many two-digits numbers are divisible by 3?
There are 25 rows of seats in an auditorium. The first row is of 20 seats, the second of 22 seats, the third of 24 seats, and so on. How many chairs are there in the 21st row ?
If Sn denote the sum of n terms of an A.P. with first term a and common difference dsuch that \[\frac{Sx}{Skx}\] is independent of x, then
The sum of n terms of an A.P. is 3n2 + 5n, then 164 is its
If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.
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.
The sum of first 16 terms of the AP: 10, 6, 2,... is ______.
An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.
Find the sum of all odd numbers between 351 and 373.
