Advertisements
Advertisements
प्रश्न
How many multiples of 4 lie between 10 and 205?
Advertisements
उत्तर
We need to find the number of multiples of 4 between 10 and 205.
So, multiples of 4 give the sequence 12, 16, ..., 204
a = 12, d = 4 and an=204">an = 204
Using the formula an=a+n-1d">an = a + (n−1)d
Plugging values in the formula we get
204=12+n-14204=12+4n-44n=196n=49">204 = 12 + (n−1)4
204 = 12 + 4n − 4
4n = 196
n = 49
Thus, there are 49 multiples of 4 between 10 and 205.
संबंधित प्रश्न
Find the sum of the following arithmetic series:
34 + 32 + 30 +...+10
Decide whether the following sequence is an A.P., if so find the 20th term of the progression:
–12, –5, 2, 9, 16, 23, 30, ..............
Select the correct alternative and write it.
What is the sum of first n natural numbers ?
Find the 23rd term of the following A.P.: 9, 4,-1,-6,-11.
Find t5 if a = 3 आणि d = −3
Decide whether the given sequence 24, 17, 10, 3, ...... is an A.P.? If yes find its common term (tn)
How many two-digit numbers are divisible by 5?
Activity :- Two-digit numbers divisible by 5 are, 10, 15, 20, ......, 95.
Here, d = 5, therefore this sequence is an A.P.
Here, a = 10, d = 5, tn = 95, n = ?
tn = a + (n − 1) `square`
`square` = 10 + (n – 1) × 5
`square` = (n – 1) × 5
`square` = (n – 1)
Therefore n = `square`
There are `square` two-digit numbers divisible by 5
Decide whether 301 is term of given sequence 5, 11, 17, 23, .....
Activity :- Here, d = `square`, therefore this sequence is an A.P.
a = 5, d = `square`
Let nth term of this A.P. be 301
tn = a + (n – 1) `square`
301 = 5 + (n – 1) × `square`
301 = 6n – 1
n = `302/6` = `square`
But n is not positive integer.
Therefore, 301 is `square` the term of sequence 5, 11, 17, 23, ......
The nth term of an A.P. 5, 8, 11, 14, ...... is 68. Find n = ?
In an A.P. if the sum of third and seventh term is zero. Find its 5th term.
