Advertisements
Advertisements
Question
How many numbers are there between 101 and 999, which are divisible by both 2 and 5?
Solution
The numbers which are divisible by both 2 and 5 are divisible by 10 also. Now, the numbers between 101 and 999 which are divisible 10 are 110, 120, 130, .., 990. Clearly, these number are in AP
Here, a = 110 and d = 120 - 110 = 10
Let this AP contains n terms. Then,
an = 990
⇒ 110+(n-1) × 10 = 990 [an = a+ (n-1) d]
⇒ 10n + 100 =990
⇒ 10n = 990 -100 = 890
⇒ n =89
Hence, there are 89 numbers between 101 and 999 which are divisible by both 2 and 5.
APPEARS IN
RELATED QUESTIONS
Find the sum 25 + 28 + 31 + ….. + 100
How many terms of the A.P. : 24, 21, 18, ................ must be taken so that their sum is 78?
Write an A.P. whose first term is a and common difference is d in the following.
a = –3, d = 0
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).
If the sum of a certain number of terms starting from first term of an A.P. is 25, 22, 19, ..., is 116. Find the last term.
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − kSn−1 + Sn−2, then k =
Find the sum:
1 + (–2) + (–5) + (–8) + ... + (–236)
In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k.
In a ‘Mahila Bachat Gat’, Kavita invested from the first day of month ₹ 20 on first day, ₹ 40 on second day and ₹ 60 on third day. If she saves like this, then what would be her total savings in the month of February 2020?
The sum of n terms of an A.P. is 3n2. The second term of this A.P. is ______.
