Advertisements
Advertisements
प्रश्न
The Sum of first five multiples of 3 is ______.
विकल्प
45
55
15
75
Advertisements
उत्तर
The Sum of first five multiples of 3 is 45.
Explanation:-
The given sequence is 3, 6, 9,...
Here,
a = 3
d = 3
n = 5
Therefore,
`"S"_n = n/2 (2a + (n - 1) d)`
`"S"_5 = 5/2 (2a + (5 - 1) d)`
= `5/2 (2(3) + 4(3))`
= `5/2 (6 + 12)`
= `5/2 (18)`
= 5 × 9
= 45
APPEARS IN
संबंधित प्रश्न
If the ratio of the sum of first n terms of two A.P’s is (7n +1): (4n + 27), find the ratio of their mth terms.
The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x.
The sum of n, 2n, 3n terms of an A.P. are S1 , S2 , S3 respectively. Prove that S3 = 3(S2 – S1 )
Find the sum given below:
–5 + (–8) + (–11) + ... + (–230)
In an AP given a3 = 15, S10 = 125, find d and a10.
Find the sum of first 15 multiples of 8.
A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5, 1.0 cm, 1.5 cm, 2.0 cm, .... as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take `pi = 22/7`)
[Hint: Length of successive semicircles is l1, l2, l3, l4, ... with centres at A, B, A, B, ... respectively.]
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 ×(5 + 3)]
A small terrace at a football field comprises 15 steps, each of which is 50 m long and built of solid concrete. Each step has a rise of `1/4` m and a tread of `1/2` m (See figure). Calculate the total volume of concrete required to build the terrace.
[Hint: Volume of concrete required to build the first step = `1/4 xx 1/2 xx 50 m^3`]
Find the sum of the following arithmetic progressions
`(x - y)^2,(x^2 + y^2), (x + y)^2,.... to n term`
Find the sum of all integers between 50 and 500, which are divisible by 7.
Find the sum of first 12 natural numbers each of which is a multiple of 7.
The sum of n natural numbers is 5n2 + 4n. Find its 8th term.
The 4th term of an AP is 11. The sum of the 5th and 7th terms of this AP is 34. Find its common difference
Write the next term of the AP `sqrt(2) , sqrt(8) , sqrt(18),.........`
Find the sum of first n terms of an AP whose nth term is (5 - 6n). Hence, find the sum of its first 20 terms.
Find the first term and common difference for the A.P.
`1/4,3/4,5/4,7/4,...`
For an given A.P., t7 = 4, d = −4, then a = ______.
Choose the correct alternative answer for the following question .
If for any A.P. d = 5 then t18 – t13 = ....
The first term of an A. P. is 5 and the common difference is 4. Complete the following activity and find the sum of the first 12 terms of the A. P.
a = 5, d = 4, s12 = ?
`s_n = n/2 [ square ]`
`s_12 = 12/2 [10 +square]`
`= 6 × square `
` =square`
Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.
Find the sum of the first 15 terms of each of the following sequences having nth term as xn = 6 − n .
If the sum of a certain number of terms starting from first term of an A.P. is 25, 22, 19, ..., is 116. Find the last term.
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
If in an A.P. Sn = n2p and Sm = m2p, where Sr denotes the sum of r terms of the A.P., then Sp is equal to
If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is
Let the four terms of the AP be a − 3d, a − d, a + d and a + 3d. find A.P.
Q.16
Q.19
Which term of the AP 3, 15, 27, 39, ...... will be 120 more than its 21st term?
If the second term and the fourth term of an A.P. are 12 and 20 respectively, then find the sum of first 25 terms:
Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.
The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
Find S10 if a = 6 and d = 3
Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years
The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
