Advertisements
Advertisements
प्रश्न
Find the sum of numbers between 1 to 140, divisible by 4.
Advertisements
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, `S_n = n/2 [2a + (n - 1)d]`
∴ `S_35 = 35/2 [2 xx 4 + (35 - 1)4]`
= `35/2 [8 + (34)4]`
= `35/2 [8 + 136]`
= `35/2 xx 144`
= 35 × 72
S35 = 2520
∴ The sum of numbers between 1 to 140, which are divisible by 4 is 2520.
APPEARS IN
संबंधित प्रश्न
Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.
In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms.
The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120
The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.
Find the sum of the following arithmetic progressions:
`(x - y)/(x + y), (3x - 2y)/(x + y), (5x - 3y)/(x + y),...` to n terms
Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,
Find the sum of the first 13 terms of the A.P: -6, 0, 6, 12,....
Find the sum of all 3-digit natural numbers, which are multiples of 11.
The 4th term of an AP is zero. Prove that its 25th term is triple its 11th term.
In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.
The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.
In an A.P., the sum of first ten terms is −150 and the sum of its next ten terms is −550. Find the A.P.
Write the expression for the common difference of an A.P. whose first term is a and nth term is b.
Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
The sum of first ten natural number is ______.
In an A.P., if Sn = n(4n + 1), find the A.P.
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
The sum of A.P. 4, 7, 10, 13, ........ upto 20 terms is ______.
For the A.P. \[14, 16, 18, \ldots\], which values of a, d and n are used to find the sum of the first 100 terms?
