Advertisements
Advertisements
प्रश्न
Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.
Advertisements
उत्तर
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
संबंधित प्रश्न
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)]
Find how many integers between 200 and 500 are divisible by 8.
Find the sum of the following arithmetic progressions:
–26, –24, –22,... to 36 terms
If 12th term of an A.P. is –13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
Find the middle term of the AP 6, 13, 20, ..., 216.
Which term of the A.P. `20, 19 1/4, 18 1/2, 17 3/4,` ... is the first negative term?
The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.
The first three terms of an AP are respectively (3y – 1), (3y + 5) and (5y + 1), find the value of y .
Draw a triangle PQR in which QR = 6 cm, PQ = 5 cm and times the corresponding sides of ΔPQR?
In an A.P. 17th term is 7 more than its 10th term. Find the common difference.
The sequence −10, −6, −2, 2, ... is ______.
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.
Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .
Here a = 1 , d =b`[ ], t_n = 149`
tn = a + (n-1) d
∴ 149 =`[ ] ∴149 = 2n - [ ]`
∴ n =`[ ]`
Write the common difference of an A.P. whose nth term is an = 3n + 7.
If Sr denotes the sum of the first r terms of an A.P. Then , S3n: (S2n − Sn) is
The common difference of an A.P., the sum of whose n terms is Sn, is
Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h–1. The second car goes at a speed of 8 km h–1 in the first hour and thereafter increasing the speed by 0.5 km h–1 each succeeding hour. After how many hours will the two cars meet?
The sum of first ten natural number is ______.
Read the following passage:
|
India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year. |
- In which year, the production is 29,200 sets?
- Find the production in the 8th year.
OR
Find the production in first 3 years. - Find the difference of the production in 7th year and 4th year.
The 5th term and the 9th term of an Arithmetic Progression are 4 and – 12 respectively.
Find:
- the first term
- common difference
- sum of 16 terms of the AP.
