Advertisements
Advertisements
प्रश्न
How many three-digit numbers are divisible by 9?
Advertisements
उत्तर
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
संबंधित प्रश्न
In an AP, given a = 7, a13 = 35, find d and S13.
In an AP given d = 5, S9 = 75, find a and a9.
The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
A ladder has rungs 25 cm apart. (See figure). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2 `1/2` m apart, what is the length of the wood required for the rungs?
[Hint: number of rungs = `250/25+ 1`]
Find the 12th term from the end of the following arithmetic progressions:
3, 5, 7, 9, ... 201
Find the three numbers in AP whose sum is 15 and product is 80.
If the numbers (2n – 1), (3n+2) and (6n -1) are in AP, find the value of n and the numbers
The nth term of an AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?
In an A.P. sum of three consecutive terms is 27 and their product is 504, find the terms.
(Assume that three consecutive terms in A.P. are a – d, a, a + d).
Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.
Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .
In an A.P., the first term is 22, nth term is −11 and the sum to first n terms is 66. Find n and d, the common difference
In an A.P., the sum of first ten terms is −150 and the sum of its next ten terms is −550. Find the A.P.
If \[\frac{1}{x + 2}, \frac{1}{x + 3}, \frac{1}{x + 5}\] are in A.P. Then, x =
Two A.P.'s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th term is
An article can be bought by paying Rs. 28,000 at once or by making 12 monthly installments. If the first installment paid is Rs. 3,000 and every other installment is Rs. 100 less than the previous one, find:
- amount of installments paid in the 9th month.
- total amount paid in the installment scheme.
Q.17
If a = 6 and d = 10, then find S10
If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, then the value of n is ______.
The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.
