Advertisements
Advertisements
प्रश्न
Find the sum of numbers between 1 to 140, divisible by 4
उत्तर
The numbers between 1 to 140 divisible by 4 are
4, 8, 12, ......, 140
The above sequence is an A.P.
∴ a = 4, d = 8 - 4 = 4
Let the number of terms in the A.P. be n.
Then, tn = 140
Since tn = a + (n – 1)d,
140 = 4 + (n – 1)(4)
∴ 140 - 4 = (n – 1)(4)
∴ 136 = (n – 1)(4)
∴ `136/4` = n - 1
∴ 34 + 1 = n
∴ n = 35
Now, Sn = `"n"/2 [2"a" + ("n" - 1)"d"]`
∴ S35 = `35/2 [2xx4+(35-1)4]`
= `35/2[8+(34)4]`
= `35/2[8+136]`
= `35/2xx144`
= 35 × 72
S35 = 2520
∴ The sum of numbers between 1 to 140, which are divisible by 4 is 2520.
APPEARS IN
संबंधित प्रश्न
Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120
How many terms of the series 54, 51, 48, …. be taken so that their sum is 513 ? Explain the double answer
Check whether -150 is a term of the A.P. 11, 8, 5, 2, ....
In an AP, given a = 2, d = 8, and Sn = 90, find n and an.
If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is, S1)? What is the sum of the first two terms? What is the second term? Similarly, find the 3rd, the 10th, and the nth terms.
The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?
Find the sum of the following Aps:
9, 7, 5, 3 … to 14 terms
Choose the correct alternative answer for the following question .
What is the sum of the first 30 natural numbers ?
Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.
There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.
Find the sum of all 2 - digit natural numbers divisible by 4.
If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
Let the four terms of the AP be a − 3d, a − d, a + d and a + 3d. find A.P.
Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.
If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be ______.
If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be ______.
The sum of first ten natural number is ______.
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k.
If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
