Advertisements
Advertisements
Question
Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.
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
In an AP Given a12 = 37, d = 3, find a and S12.
Find the sum of all even integers between 101 and 999.
If numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n and its next two terms.
Find the sum of two middle most terms of the AP `-4/3, -1 (-2)/3,..., 4 1/3.`
If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.
The sum of three numbers in AP is 3 and their product is -35. Find the numbers.
Find the sum of all natural numbers between 200 and 400 which are divisible by 7.
First term and the common differences of an A.P. are 6 and 3 respectively; find S27.
Solution: First term = a = 6, common difference = d = 3, S27 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]` - Formula
Sn = `27/2 [12 + (27 - 1)square]`
= `27/2 xx square`
= 27 × 45
S27 = `square`
Two A.P.’ s are given 9, 7, 5, . . . and 24, 21, 18, . . . . If nth term of both the progressions are equal then find the value of n and nth term.
Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.
If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?
If the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is
Q.16
How many terms of the A.P. 27, 24, 21, …, should be taken so that their sum is zero?
Find the sum of numbers between 1 to 140, divisible by 4
If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, then the value of n is ______.
The sum of all odd integers between 2 and 100 divisible by 3 is ______.
Find the sum of all the 11 terms of an AP whose middle most term is 30.
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?
Solve the equation
– 4 + (–1) + 2 + ... + x = 437
