Advertisements
Advertisements
Question
Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.
Advertisements
Solution
The numbers divisible by 4 between 1 and 145 are
4, 8, 12, 16, .........144 ; which is an A. P.
Here, a = 4, d = 4, tn = 144 we have to find n.
tn = a + (n - 1) d
∴tn = 4 + (n - 1) × 4
∴ 144 = 4n
∴ n = 36
Now, `s_n = n/2[t_1+t_n]`
`∴ S_36 = 36/2 [4+144]`
= 18 × 148 = 2664
Alternate Method
4 + 8 + 12 + ..... + 144
= 4(1 + 2 + 3 + ..... + 36)
`= (4xx36xx37)/2`
= 12 × 6 × 37
= 444 × 6
= 2664
This is also possible.
∴ The sum of numbers between 1 and 145 divisible by 4 is 2664.
APPEARS IN
RELATED QUESTIONS
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
If the mth term of an A.P. is 1/n and the nth term is 1/m, show that the sum of mn terms is (mn + 1)
Find the sum of the following APs:
0.6, 1.7, 2.8, ... to 100 terms.
Find the three numbers in AP whose sum is 15 and product is 80.
If k, (2k - 1) and (2k + 1) are the three successive terms of an AP, find the value of k.
What is the sum of first n terms of the AP a, 3a, 5a, ....
How many terms of the A.P. 21, 18, 15, ... must be added to get the sum 0?
Choose the correct alternative answer for the following question .
What is the sum of the first 30 natural numbers ?
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.
If the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
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 =
If Sr denotes the sum of the first r terms of an A.P. Then , S3n: (S2n − Sn) is
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
Let the four terms of the AP be a − 3d, a − d, a + d and a + 3d. find A.P.
Q.14
Q.19
Find the sum of first 1000 positive integers.
Activity :- Let 1 + 2 + 3 + ........ + 1000
Using formula for the sum of first n terms of an A.P.,
Sn = `square`
S1000 = `square/2 (1 + 1000)`
= 500 × 1001
= `square`
Therefore, Sum of the first 1000 positive integer is `square`
The first term of an AP of consecutive integers is p2 + 1. The sum of 2p + 1 terms of this AP is ______.
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?
