Advertisements
Advertisements
प्रश्न
How many three-digit natural numbers are divisible by 9?
Advertisements
उत्तर
The three-digit natural 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
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero
Find the sum of first 8 multiples of 3
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
In an A.P., if the first term is 22, the common difference is −4 and the sum to n terms is 64, find n.
Find the sum of first 20 terms of the sequence whose nth term is `a_n = An + B`
Find the sum of 28 terms of an A.P. whose nth term is 8n – 5.
Find four numbers in AP whose sum is 8 and the sum of whose squares is 216.
Find the sum of the following Aps:
i) 2, 7, 12, 17, ……. to 19 terms .
If the common differences of an A.P. is 3, then a20 − a15 is
The sum of the first n terms of an A.P. is 3n2 + 6n. Find the nth term of this A.P.
Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.
If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is
Q.13
Q.18
Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
k + 2, 2k + 7 and 4k + 12 are the first three terms of an A.P. The first term of this A.P. is ______.
